Programs for A000001-A049999

List of integer sequences with links to LODA programs.

• A000002 (program): Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1’s and 2’s.
• A000004 (program): The zero sequence.
• A000005 (program): d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.
• A000006 (program): Integer part of square root of n-th prime.
• A000007 (program): The characteristic function of {0}: a(n) = 0^n.
• A000008 (program): Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.
• A000009 (program): Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.
• A000010 (program): Euler totient function phi(n): count numbers <= n and prime to n.
• A000011 (program): Number of n-bead necklaces (turning over is allowed) where complements are equivalent.
• A000012 (program): The simplest sequence of positive numbers: the all 1’s sequence.
• A000013 (program): Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed.
• A000015 (program): Smallest prime power >= n.
• A000016 (program): a(n) is the number of distinct (infinite) output sequences from binary n-stage shift register which feeds back the complement of the last stage.
• A000023 (program): Expansion of e.g.f. exp(-2*x)/(1-x).
• A000026 (program): Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).
• A000027 (program): The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.
• A000028 (program): Let n = p_1^e_1 p_2^e_2 p_3^e_3 … be the prime factorization of n. Sequence gives n such that the sum of the numbers of 1’s in the binary expansions of e_1, e_2, e_3, … is odd.
• A000029 (program): Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).
• A000030 (program): Initial digit of n.
• A000031 (program): Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.
• A000032 (program): Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1.
• A000033 (program): Coefficients of ménage hit polynomials.
• A000034 (program): Period 2: repeat [1, 2]; a(n) = 1 + (n mod 2).
• A000035 (program): Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.
• A000037 (program): Numbers that are not squares (or, the nonsquares).
• A000038 (program): Twice A000007.
• A000040 (program): The prime numbers.
• A000041 (program): a(n) is the number of partitions of n (the partition numbers).
• A000042 (program): Unary representation of natural numbers.
• A000044 (program): Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1) + a(n-2) - a(n-13).
• A000045 (program): Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
• A000048 (program): Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.
• A000051 (program): a(n) = 2^n + 1.
• A000056 (program): Order of the group SL(2,Z_n).
• A000062 (program): A Beatty sequence: a(n) = floor(n/(e-2)).
• A000064 (program): Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents.
• A000065 (program): -1 + number of partitions of n.
• A000068 (program): Numbers k such that k^4 + 1 is prime.
• A000069 (program): Odious numbers: numbers with an odd number of 1’s in their binary expansion.
• A000070 (program): a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).
• A000071 (program): a(n) = Fibonacci(n) - 1.
• A000073 (program): Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3 with a(0) = a(1) = 0 and a(2) = 1.
• A000078 (program): Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) for n >= 4 with a(0) = a(1) = a(2) = 0 and a(3) = 1.
• A000079 (program): Powers of 2: a(n) = 2^n.
• A000082 (program): a(n) = n^2*Product_{p|n} (1 + 1/p).
• A000085 (program): Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.
• A000086 (program): Number of solutions to x^2 - x + 1 == 0 (mod n).
• A000089 (program): Number of solutions to x^2 + 1 == 0 (mod n).
• A000090 (program): Expansion of e.g.f. exp((-x^3)/3)/(1-x).
• A000093 (program): a(n) = floor(n^(3/2)).
• A000094 (program): Number of trees of diameter 4.
• A000095 (program): Number of fixed points of GAMMA_0 (n) of type i.
• A000096 (program): a(n) = n*(n+3)/2.
• A000097 (program): Number of partitions of n if there are two kinds of 1’s and two kinds of 2’s.
• A000100 (program): a(n) is the number of compositions of n in which the maximal part is 3.
• A000102 (program): a(n) = number of compositions of n in which the maximum part size is 4.
• A000108 (program): Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
• A000110 (program): Bell or exponential numbers: number of ways to partition a set of n labeled elements.
• A000111 (program): Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250).
• A000114 (program): Number of cusps of principal congruence subgroup GAMMA^{hat}(n).
• A000115 (program): Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).
• A000116 (program): Number of even sequences with period 2n (bisection of A000013).
• A000117 (program): Number of even sequences with period 2n (bisection of A000011).
• A000118 (program): Number of ways of writing n as a sum of 4 squares; also theta series of four-dimensional cubic lattice Z^4.
• A000120 (program): 1’s-counting sequence: number of 1’s in binary expansion of n (or the binary weight of n).
• A000122 (program): Expansion of Jacobi theta function theta_3(x) = Sum_{m =-oo..oo} x^(m^2) (number of integer solutions to k^2 = n).
• A000123 (program): Number of binary partitions: number of partitions of 2n into powers of 2.
• A000124 (program): Central polygonal numbers (the Lazy Caterer’s sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.
• A000125 (program): Cake numbers: maximal number of pieces resulting from n planar cuts through a cube (or cake): C(n+1,3) + n + 1.
• A000126 (program): A nonlinear binomial sum.
• A000127 (program): Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes.
• A000128 (program): A nonlinear binomial sum.
• A000129 (program): Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
• A000132 (program): Number of ways of writing n as a sum of 5 squares.
• A000134 (program): Positive zeros of Bessel function of order 0 rounded to nearest integer.
• A000138 (program): Expansion of e.g.f. exp(-x^4/4)/(1-x).
• A000139 (program): a(n) = 2*(3*n)!/((2*n+1)!*((n+1)!)).
• A000141 (program): Number of ways of writing n as a sum of 6 squares.
• A000142 (program): Factorial numbers: n! = 1*2*3*4*…*n (order of symmetric group S_n, number of permutations of n letters).
• A000143 (program): Number of ways of writing n as a sum of 8 squares.
• A000144 (program): Number of ways of writing n as a sum of 10 squares.
• A000145 (program): Number of ways of writing n as a sum of 12 squares.
• A000149 (program): a(n) = floor(e^n).
• A000150 (program): Number of dissections of an n-gon, rooted at an exterior edge, asymmetric with respect to that edge.
• A000152 (program): Number of ways of writing n as a sum of 16 squares.
• A000153 (program): a(n) = n*a(n-1) + (n-2)*a(n-2), with a(0) = 0, a(1) = 1.
• A000155 (program): Nearest integer to modified Bessel function K_n(1).
• A000156 (program): Number of ways of writing n as a sum of 24 squares.
• A000159 (program): Coefficients of ménage hit polynomials.
• A000161 (program): Number of partitions of n into 2 squares.
• A000165 (program): Double factorial of even numbers: (2n)!! = 2^n*n!.
• A000166 (program): Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
• A000167 (program): Nearest integer to modified Bessel function K_n(2).
• A000168 (program): a(n) = 2*3^n*(2*n)!/(n!*(n+2)!).
• A000169 (program): Number of labeled rooted trees with n nodes: n^(n-1).
• A000172 (program): Franel number a(n) = Sum_{k = 0..n} binomial(n,k)^3.
• A000178 (program): Superfactorials: product of first n factorials.
• A000179 (program): Ménage numbers: a(0) = 1, a(1) = -1, and for n >= 2, a(n) = number of permutations s of [0, …, n-1] such that s(i) != i and s(i) != i+1 (mod n) for all i.
• A000180 (program): Expansion of E.g.f. exp(-x)/(1-3x).
• A000181 (program): Coefficients of ménage hit polynomials.
• A000182 (program): Tangent (or “Zag”) numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).
• A000184 (program): Number of genus 0 rooted maps with 3 faces with n vertices.
• A000185 (program): Coefficients of ménage hit polynomials.
• A000188 (program): (1) Number of solutions to x^2 == 0 (mod n). (2) Also square root of largest square dividing n. (3) Also max_{ d divides n } gcd(d, n/d).
• A000189 (program): Number of solutions to x^3 == 0 (mod n).
• A000190 (program): Number of solutions to x^4 == 0 (mod n).
• A000193 (program): Nearest integer to log n.
• A000194 (program): n appears 2n times, for n >= 1; also nearest integer to square root of n.
• A000195 (program): a(n) = floor(log(n)).
• A000196 (program): Integer part of square root of n. Or, number of positive squares <= n. Or, n appears 2n+1 times.
• A000201 (program): Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.
• A000202 (program): a(8i+j) = 13i + a(j), where 1<=j<=8.
• A000203 (program): a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).
• A000204 (program): Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.
• A000210 (program): A Beatty sequence: floor(n*(e-1)).
• A000211 (program): a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.
• A000212 (program): a(n) = floor(n^2/3).
• A000213 (program): Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.
• A000216 (program): Take sum of squares of digits of previous term, starting with 2.
• A000217 (program): Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + … + n.
• A000218 (program): Take sum of squares of digits of previous term; start with 3.
• A000219 (program): Number of planar partitions (or plane partitions) of n.
• A000221 (program): Take sum of squares of digits of previous term; start with 5.
• A000222 (program): Coefficients of ménage hit polynomials.
• A000225 (program): a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
• A000227 (program): Nearest integer to e^n.
• A000240 (program): Rencontres numbers: number of permutations of [n] with exactly one fixed point.
• A000241 (program): Crossing number of complete graph with n nodes.
• A000244 (program): Powers of 3: a(n) = 3^n.
• A000245 (program): a(n) = 3*(2*n)!/((n+2)!*(n-1)!).
• A000246 (program): Number of permutations in the symmetric group S_n that have odd order.
• A000247 (program): a(n) = 2^n - n - 2.
• A000248 (program): Expansion of e.g.f. exp(x*exp(x)).
• A000252 (program): Number of invertible 2 X 2 matrices mod n.
• A000253 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-3) + 2^(n-1).
• A000254 (program): Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.
• A000255 (program): a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.
• A000257 (program): Number of rooted bicubic maps: a(n) = (8*n-4)*a(n-1)/(n+2) for n >= 2, a(0) = a(1) = 1.
• A000259 (program): Number of certain rooted planar maps.
• A000260 (program): Number of rooted simplicial 3-polytopes with n+3 nodes; or rooted 3-connected triangulations with 2n+2 faces; or rooted 3-connected trivalent maps with 2n+2 vertices.
• A000261 (program): a(n) = n*a(n-1) + (n-3)*a(n-2), with a(1) = 0, a(2) = 1.
• A000262 (program): Number of “sets of lists”: number of partitions of {1,…,n} into any number of lists, where a list means an ordered subset.
• A000265 (program): Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.
• A000266 (program): Expansion of e.g.f. exp(-x^2/2) / (1-x).
• A000267 (program): Integer part of square root of 4n+1.
• A000270 (program): For n >= 2, a(n) = b(n+1)+b(n)+b(n-1), where the b(i) are the ménage numbers A000179; a(0)=a(1)=1.
• A000271 (program): Sums of ménage numbers.
• A000272 (program): Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
• A000274 (program): Number of permutations of length n with 2 consecutive ascending pairs.
• A000275 (program): Coefficients of a Bessel function (reciprocal of J_0(z)); also pairs of permutations with rise/rise forbidden.
• A000276 (program): Associated Stirling numbers.
• A000277 (program): 3*n - 2*floor(sqrt(4*n+5)) + 5.
• A000278 (program): a(n) = a(n-1) + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
• A000279 (program): Card matching: coefficients B[n,1] of t in the reduced hit polynomial An,n,n.
• A000280 (program): a(n) = a(n-1) + a(n-2)^3.
• A000281 (program): Expansion of cos(x)/cos(2x).
• A000283 (program): a(n) = a(n-1)^2 + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
• A000285 (program): a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.
• A000288 (program): Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
• A000289 (program): A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).
• A000290 (program): The squares: a(n) = n^2.
• A000292 (program): Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.
• A000294 (program): Expansion of g.f. Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).
• A000295 (program): Eulerian numbers (Euler’s triangle: column k=2 of A008292, column k=1 of A173018).
• A000296 (program): Set partitions without singletons: number of partitions of an n-set into blocks of size > 1. Also number of cyclically spaced (or feasible) partitions.
• A000297 (program): a(n) = (n+1)*(n+3)*(n+8)/6.
• A000301 (program): a(n) = a(n-1)*a(n-2) with a(0) = 1, a(1) = 2; also a(n) = 2^Fibonacci(n).
• A000302 (program): Powers of 4: a(n) = 4^n.
• A000304 (program): a(n) = a(n-1)*a(n-2).
• A000305 (program): Number of certain rooted planar maps.
• A000308 (program): a(n) = a(n-1)*a(n-2)*a(n-3) with a(1)=1, a(2)=2 and a(3)=3.
• A000309 (program): Number of rooted planar bridgeless cubic maps with 2n nodes.
• A000312 (program): a(n) = n^n; number of labeled mappings from n points to themselves (endofunctions).
• A000313 (program): Number of permutations of length n with 3 consecutive ascending pairs.
• A000316 (program): Two decks each have n kinds of cards, 2 of each kind. The first deck is laid out in order. The second deck is shuffled and laid out next to the first. A match occurs if a card from the second deck is next to a card of the same kind from the first deck. a(n) is the number of ways of achieving no matches.
• A000317 (program): a(n+1) = a(n)^2 - a(n) a(n-1) + a(n-1)^2.
• A000318 (program): Generalized tangent numbers d(4,n).
• A000321 (program): H_n(-1/2), where H_n(x) is Hermite polynomial of degree n.
• A000322 (program): Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
• A000325 (program): a(n) = 2^n - n.
• A000326 (program): Pentagonal numbers: a(n) = n*(3*n-1)/2.
• A000328 (program): Number of points of norm <= n^2 in square lattice.
• A000330 (program): Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + … + n^2 = n*(n+1)*(2*n+1)/6.
• A000332 (program): Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24.
• A000335 (program): Euler transform of A000292.
• A000336 (program): a(n) = a(n-1)*a(n-2)*a(n-3)*a(n-4); for n < 5, a(n) = n.
• A000337 (program): a(n) = (n-1)*2^n + 1.
• A000338 (program): Expansion of x^3*(5-2*x)*(1-x^3)/(1-x)^4.
• A000340 (program): a(0)=1, a(n) = 3*a(n-1) + n + 1.
• A000344 (program): a(n) = 5*binomial(2n, n-2)/(n+3).
• A000346 (program): a(n) = 2^(2*n+1) - binomial(2*n+1, n+1).
• A000351 (program): Powers of 5: a(n) = 5^n.
• A000352 (program): One half of the number of permutations of [n] such that the differences have three runs with the same signs.
• A000354 (program): Expansion of e.g.f. exp(-x)/(1-2*x).
• A000356 (program): Number of rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle: (2n)!(2n+1)! / (n!^2*(n+1)!(n+2)!).
• A000358 (program): Number of binary necklaces of length n with no subsequence 00, excluding the necklace “0”.
• A000360 (program): Distribution of nonempty triangles inside a fractal rep-4-tile.
• A000363 (program): Number of permutations of [n] with exactly 2 increasing runs of length at least 2.
• A000364 (program): Euler (or secant or “Zig”) numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).
• A000367 (program): Numerators of Bernoulli numbers B_2n.
• A000377 (program): Expansion of f(-q^3) * f(-q^8) * chi(-q^12) / chi(-q) in powers of q where chi(), f() are Ramanujan theta functions.
• A000378 (program): Sums of three squares: numbers of the form x^2 + y^2 + z^2.
• A000379 (program): Numbers n where total number of 1-bits in the exponents of their prime factorization is even; a 2-way classification of integers: complement of A000028.
• A000382 (program): Restricted permutations.
• A000383 (program): Hexanacci numbers with a(0) = … = a(5) = 1.
• A000384 (program): Hexagonal numbers: a(n) = n*(2*n-1).
• A000385 (program): Convolution of A000203 with itself.
• A000386 (program): Coefficients of ménage hit polynomials.
• A000387 (program): Rencontres numbers: number of permutations of [n] with exactly two fixed points.
• A000389 (program): Binomial coefficients C(n,5).
• A000392 (program): Stirling numbers of second kind S(n,3).
• A000394 (program): Numbers of form x^2 + y^2 + 7z^2.
• A000399 (program): Unsigned Stirling numbers of first kind s(n,3).
• A000400 (program): Powers of 6: a(n) = 6^n.
• A000401 (program): Numbers of form x^2 + y^2 + 2z^2.
• A000404 (program): Numbers that are the sum of 2 nonzero squares.
• A000407 (program): a(n) = (2*n+1)! / n!.
• A000408 (program): Numbers that are the sum of three nonzero squares.
• A000414 (program): Numbers that are the sum of 4 nonzero squares.
• A000415 (program): Numbers that are the sum of 2 but no fewer nonzero squares.
• A000420 (program): Powers of 7: a(n) = 7^n.
• A000422 (program): Concatenation of numbers from n down to 1.
• A000423 (program): a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.
• A000424 (program): Differences of reciprocals of unity.
• A000425 (program): Coefficients of ménage hit polynomials.
• A000426 (program): Coefficients of ménage hit polynomials.
• A000430 (program): Primes and squares of primes.
• A000431 (program): Expansion of 2*x^3/((1-2*x)^2*(1-4*x)).
• A000433 (program): n written in base where place values are positive cubes.
• A000435 (program): Normalized total height of all nodes in all rooted trees with n labeled nodes.
• A000436 (program): Generalized Euler numbers c(3,n).
• A000439 (program): Powers of rooted tree enumerator.
• A000441 (program): a(n) = Sum_{k=1..n-1} k*sigma(k)*sigma(n-k).
• A000442 (program): a(n) = (n!)^3.
• A000447 (program): a(n) = 1^2 + 3^2 + 5^2 + 7^2 + … + (2*n-1)^2 = n*(4*n^2 - 1)/3.
• A000449 (program): Rencontres numbers: number of permutations of [n] with exactly 3 fixed points.
• A000450 (program): Coefficients of ménage hit polynomials.
• A000452 (program): The greedy sequence of integers which avoids 3-term geometric progressions.
• A000453 (program): Stirling numbers of the second kind, S(n,4).
• A000454 (program): Unsigned Stirling numbers of first kind s(n,4).
• A000457 (program): Exponential generating function: (1+3*x)/(1-2*x)^(7/2).
• A000459 (program): Number of multiset permutations of {1, 1, 2, 2, …, n, n} with no fixed points.
• A000460 (program): Eulerian numbers (Euler’s triangle: column k=3 of A008292, column k=2 of A173018).
• A000461 (program): Concatenate n n times.
• A000462 (program): Numbers written in base of triangular numbers.
• A000463 (program): n followed by n^2.
• A000464 (program): Expansion of sin x /cos 2x.
• A000466 (program): a(n) = 4*n^2 - 1.
• A000468 (program): Powers of ten written in base 8.
• A000469 (program): 1 together with products of 2 or more distinct primes.
• A000471 (program): a(n) = floor(sinh(n)).
• A000475 (program): Rencontres numbers: number of permutations of [n] with exactly 4 fixed points.
• A000477 (program): a(n) = Sum_{k=1..n-1} k^2*sigma(k)*sigma(n-k).
• A000478 (program): Number of ways of placing n labeled balls into 3 indistinguishable boxes with at least 2 balls in each box.
• A000480 (program): a(n) = floor(cos(n)).
• A000481 (program): Stirling numbers of the second kind, S(n,5).
• A000482 (program): Unsigned Stirling numbers of first kind s(n,5).
• A000483 (program): Associated Stirling numbers: second order reciprocal Stirling numbers (Fekete) [[n, 3]]. The number of 3-orbit permutations of an n-set with at least 2 elements in each orbit.
• A000486 (program): One half of the number of permutations of [n] such that the differences have 4 runs with the same signs.
• A000487 (program): Number of permutations of length n with exactly two valleys.
• A000490 (program): Generalized Euler numbers c(4,n).
• A000493 (program): a(n) = floor(sin(n)).
• A000495 (program): Nearest integer to sinh(n).
• A000497 (program): S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind.
• A000498 (program): Eulerian numbers (Euler’s triangle: column k=4 of A008292, column k=3 of A173018)
• A000499 (program): a(n) = Sum_{k=1..n-1} k^3*sigma(k)*sigma(n-k).
• A000501 (program): a(n) = floor(cosh(n)).
• A000505 (program): Eulerian numbers (Euler’s triangle: column k=5 of A008292, column k=4 of A173018).
• A000514 (program): Eulerian numbers (Euler’s triangle: column k=6 of A008292, column k=5 of A173018)
• A000515 (program): a(n) = (2n)!(2n+1)!/n!^4, or equally (2n+1)*binomial(2n,n)^2.
• A000520 (program): Nearest integer to log_10(n).
• A000522 (program): Total number of ordered k-tuples (k=0..n) of distinct elements from an n-element set: a(n) = Sum_{k=0..n} n!/k!.
• A000523 (program): a(n) = floor(log_2(n)).
• A000529 (program): Powers of rooted tree enumerator.
• A000531 (program): From area of cyclic polygon of 2n + 1 sides.
• A000533 (program): a(0)=1; a(n) = 10^n + 1, n >= 1.
• A000536 (program): Number of 3-line Latin rectangles.
• A000537 (program): Sum of first n cubes; or n-th triangular number squared.
• A000538 (program): Sum of fourth powers: 0^4 + 1^4 + … + n^4.
• A000539 (program): Sum of 5th powers: 0^5 + 1^5 + 2^5 + … + n^5.
• A000540 (program): Sum of 6th powers: 0^6 + 1^6 + 2^6 + … + n^6.
• A000541 (program): Sum of 7th powers: 1^7 + 2^7 + … + n^7.
• A000542 (program): Sum of 8th powers: 1^8 + 2^8 + … + n^8.
• A000543 (program): Number of inequivalent ways to color vertices of a cube using at most n colors.
• A000548 (program): Squares that are not the sum of 2 nonzero squares.
• A000551 (program): Number of labeled rooted trees of height 2 with n nodes.
• A000554 (program): Number of labeled trees of diameter 3 with n nodes.
• A000556 (program): Expansion of exp(-x) / (1 - exp(x) + exp(-x)).
• A000557 (program): Expansion of e.g.f.: 1/(1-2*sinh(x)).
• A000558 (program): Generalized Stirling numbers of second kind.
• A000561 (program): Number of discordant permutations.
• A000566 (program): Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2.
• A000567 (program): Octagonal numbers: n*(3*n-2). Also called star numbers.
• A000570 (program): Number of tournaments on n nodes determined by their score vectors.
• A000572 (program): A Beatty sequence: [ n(e+1) ].
• A000574 (program): Coefficient of x^5 in expansion of (1 + x + x^2)^n.
• A000575 (program): Tenth column of quintinomial coefficients.
• A000578 (program): The cubes: a(n) = n^3.
• A000579 (program): Figurate numbers or binomial coefficients C(n,6).
• A000580 (program): a(n) = binomial coefficient C(n,7).
• A000581 (program): a(n) = binomial coefficient C(n,8).
• A000582 (program): a(n) = binomial coefficient C(n,9).
• A000583 (program): Fourth powers: a(n) = n^4.
• A000584 (program): Fifth powers: a(n) = n^5.
• A000586 (program): Number of partitions of n into distinct primes.
• A000587 (program): Rao Uppuluri-Carpenter numbers (or complementary Bell numbers): e.g.f. = exp(1 - exp(x)).
• A000588 (program): a(n) = 7*binomial(2n,n-3)/(n+4).
• A000589 (program): a(n) = 11*binomial(2n,n-5)/(n+6).
• A000590 (program): a(n) = 13*binomial(2n,n-6)/(n+7).
• A000592 (program): Number of nonnegative solutions of x^2 + y^2 = z in first n shells.
• A000593 (program): Sum of odd divisors of n.
• A000594 (program): Ramanujan’s tau function (or Ramanujan numbers, or tau numbers).
• A000596 (program): Central factorial numbers.
• A000601 (program): Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).
• A000603 (program): Number of nonnegative solutions to x^2 + y^2 <= n^2.
• A000604 (program): Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.
• A000606 (program): Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.
• A000607 (program): Number of partitions of n into prime parts.
• A000629 (program): Number of necklaces of partitions of n+1 labeled beads.
• A000643 (program): a(n) = a(n-1) + 2^a(n-2).
• A000655 (program): a(n) = number of letters in a(n-1), a(1) = 1 (in English).
• A000657 (program): Median Euler numbers (the middle numbers of Arnold’s shuttle triangle).
• A000660 (program): Boustrophedon transform of 1,1,2,3,4,5,…
• A000667 (program): Boustrophedon transform of all-1’s sequence.
• A000670 (program): Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].
• A000674 (program): Boustrophedon transform of 1, 2, 2, 2, 2, …
• A000680 (program): a(n) = (2n)!/2^n.
• A000681 (program): Number of n X n matrices with nonnegative entries and every row and column sum 2.
• A000683 (program): Number of colorings of labeled graphs on n nodes using exactly 2 colors, divided by 4.
• A000684 (program): Number of colored labeled n-node graphs with 2 interchangeable colors.
• A000687 (program): Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,…
• A000688 (program): Number of Abelian groups of order n; number of factorizations of n into prime powers.
• A000689 (program): Final decimal digit of 2^n.
• A000695 (program): Moser-de Bruijn sequence: sums of distinct powers of 4.
• A000698 (program): A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!.
• A000700 (program): Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes.
• A000701 (program): One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes.
• A000703 (program): Chromatic number (or Heawood number) of nonorientable surface with n crosscaps.
• A000704 (program): Number of degree-n even permutations of order dividing 2.
• A000707 (program): Number of permutations of [1,2,…,n] with n-1 inversions.
• A000708 (program): a(n) = E(n+1) - 2*E(n), where E(i) is the Euler number A000111(i).
• A000712 (program): Generating function = Product_{m>=1} 1/(1 - x^m)^2; a(n) = number of partitions of n into parts of 2 kinds.
• A000713 (program): EULER transform of 3, 2, 2, 2, 2, 2, 2, 2, …
• A000714 (program): Number of partitions of n, with three kinds of 1 and 2 and two kinds of 3,4,5,….
• A000716 (program): Number of partitions of n into parts of 3 kinds.
• A000720 (program): pi(n), the number of primes <= n. Sometimes called PrimePi(n) to distinguish it from the number 3.14159…
• A000726 (program): Number of partitions of n in which no parts are multiples of 3.
• A000727 (program): Expansion of Product_{k >= 1} (1 - x^k)^4.
• A000728 (program): Expansion of Product_{n>=1} (1-x^n)^5.
• A000729 (program): Expansion of Product_{k >= 1} (1 - x^k)^6.
• A000730 (program): Expansion of Product_{n>=1} (1 - x^n)^7.
• A000731 (program): Expansion of Product (1 - x^k)^8 in powers of x.
• A000734 (program): Boustrophedon transform of 1,1,2,4,8,16,32,…
• A000735 (program): Expansion of Product_{k>=1} (1 - x^k)^12.
• A000737 (program): Boustrophedon transform of natural numbers, cf. A000027.
• A000738 (program): Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,…
• A000739 (program): Expansion of Product_{k>=1} (1 - x^k)^16.
• A000740 (program): Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement; also Dirichlet convolution of b_n=2^(n-1) with mu(n); also number of components of Mandelbrot set corresponding to Julia sets with an attractive n-cycle.
• A000741 (program): Number of compositions of n into 3 ordered relatively prime parts.
• A000744 (program): Boustrophedon transform (second version) of Fibonacci numbers 1,1,2,3,…
• A000745 (program): Boustrophedon transform of squares.
• A000746 (program): Boustrophedon transform of triangular numbers.
• A000748 (program): Expansion of bracket function.
• A000749 (program): a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n > 3, with a(0)=a(1)=a(2)=0, a(3)=1.
• A000750 (program): Expansion of bracket function.
• A000752 (program): Boustrophedon transform of powers of 2.
• A000754 (program): Boustrophedon transform of odd numbers.
• A000756 (program): Boustrophedon transform of sequence 1,1,0,0,0,0,…
• A000757 (program): Number of cyclic permutations of [n] with no i->i+1 (mod n)
• A000770 (program): Stirling numbers of the second kind, S(n,6).
• A000771 (program): Stirling numbers of second kind, S(n,7).
• A000773 (program): Number of numbers == 0 (mod 3) in range 2^n to 2^(n+1) with odd number of 1’s in binary expansion.
• A000774 (program): a(n) = n!*(1 + Sum_{i=1..n} 1/i).
• A000775 (program): a(n) = n! * (n + 1 + 2*Sum_{k=1…n} 1/k).
• A000776 (program): a(n) = n! * (1 + 2*Sum_{k=1..n} 1/k).
• A000777 (program): a(n) = (n+2)*Catalan(n) - 1.
• A000778 (program): a(n) = Catalan(n) + Catalan(n+1) - 1.
• A000779 (program): a(n) = 2*(2n-1)!!-(n-1)!*2^(n-1), where (2n-1)!! is A001147(n).
• A000780 (program): a(n) = (n+1)!/2 + (n-1)(n-1)!.
• A000781 (program): a(n) = 3*Catalan(n) - Catalan(n-1) - 1.
• A000782 (program): a(n) = 2*Catalan(n) - Catalan(n-1).
• A000788 (program): Total number of 1’s in binary expansions of 0, …, n.
• A000789 (program): Maximal order of a triangle-free cyclic graph with no independent set of size n.
• A000792 (program): a(n) = max{(n - i)*a(i) : i < n}; a(0) = 1.
• A000795 (program): Salié numbers: expansion of cosh x / cos x = Sum_{n >= 0} a(n)*x^(2n)/(2n)!.
• A000796 (program): Decimal expansion of Pi (or digits of Pi).
• A000799 (program): a(n) = floor(2^n / n).
• A000801 (program): a(n) = Sum_{k = 1..n} floor(2^k / k).
• A000803 (program): a(n+3) = a(n+2) + a(n+1) + a(n) - 4.
• A000806 (program): Bessel polynomial y_n(-1).
• A000807 (program): Quadratic invariants.
• A000810 (program): Expansion of e.g.f. (sin x + cos x)/cos 3x.
• A000816 (program): E.g.f.: Sum_{n >= 0} a(n) * x^(2*n) / (2*n)! = sin(x)^2 / cos(2*x).
• A000819 (program): E.g.f.: cos(x)^2 / cos(2x) = Sum_{n >= 0} a(n) * x^(2n) / (2n)!.
• A000828 (program): E.g.f. cos(x)/(cos(x) - sin(x)).
• A000831 (program): Expansion of e.g.f. (1 + tan(x))/(1 - tan(x)).
• A000834 (program): Expansion of exp(x)*(1 + tan(x))/(1 - tan(x)).
• A000846 (program): a(n) = C(3n,n) - C(2n,n).
• A000855 (program): Final two digits of 2^n.
• A000865 (program): Numbers beginning with letter ‘o’ in English.
• A000866 (program): 2^n written in base 5.
• A000879 (program): Number of primes < prime(n)^2.
• A000888 (program): a(n) = (2*n)!^2 / ((n+1)!*n!^3).
• A000891 (program): a(n) = (2*n)!*(2*n+1)! / (n! * (n+1)!)^2.
• A000894 (program): a(n) = (2*n)!*(2*n+1)! /((n+1)! *n!^3).
• A000897 (program): a(n) = (4*n)! / ((2*n)!*n!^2).
• A000898 (program): a(n) = 2*(a(n-1) + (n-1)*a(n-2)) for n >= 2 with a(0) = 1.
• A000900 (program): Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
• A000902 (program): Expansion of e.g.f. (1/2)*(exp(2*x + x^2) + 1).
• A000904 (program): a(n) = (n+1)*a(n-1) + (n+2)*a(n-2) + a(n-3); a(1)=0, a(2)=3, a(3)=13.
• A000906 (program): Exponential generating function: 2*(1+3*x)/(1-2*x)^(7/2).
• A000907 (program): Second order reciprocal Stirling number (Fekete) [[2n+2, n]]. The number of n-orbit permutations of a (2n+2)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).
• A000909 (program): a(n) = (2n)!(2n+1)! / n!^2.
• A000910 (program): a(n) = 5*binomial(n, 6).
• A000911 (program): a(n) = (2n+3)! /( n! * (n+1)! ).
• A000912 (program): Expansion of (sqrt(1-4x^2) - sqrt(1-4x))/(2x).
• A000914 (program): Stirling numbers of the first kind: s(n+2, n).
• A000915 (program): Stirling numbers of first kind s(n+4, n).
• A000917 (program): a(n) = (2n+3)!/(n!*(n+2)!).
• A000918 (program): a(n) = 2^n - 2.
• A000919 (program): a(n) = 4^n - C(4,3)*3^n + C(4,2)*2^n - C(4,1).
• A000920 (program): Differences of 0: 6!*Stirling2(n,6).
• A000925 (program): Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers.
• A000930 (program): Narayana’s cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3).
• A000931 (program): Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0.
• A000932 (program): a(n) = a(n-1) + n*a(n-2); a(0) = a(1) = 1.
• A000933 (program): Genus of complete graph on n nodes.
• A000934 (program): Chromatic number (or Heawood number) Chi(n) of surface of genus n.
• A000943 (program): Number of combinatorial types of simplicial n-dimensional polytopes with n+3 nodes.
• A000952 (program): Numbers n == 2 (mod 4) that are the orders of conference matrices.
• A000957 (program): Fine’s sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n nodes having root of even degree.
• A000958 (program): Number of ordered rooted trees with n edges having root of odd degree.
• A000960 (program): Flavius Josephus’s sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.
• A000961 (program): Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).
• A000964 (program): The convergent sequence C_n for the ternary continued fraction (3,1;2,2) of period 2.
• A000966 (program): n! never ends in this many 0’s.
• A000968 (program): Sum of odd Fermat coefficients rounded to nearest integer.
• A000969 (program): Expansion of (1+x+2*x^2)/((1-x)^2*(1-x^3)).
• A000970 (program): Fermat coefficients.
• A000971 (program): Fermat coefficients.
• A000972 (program): Fermat coefficients.
• A000973 (program): Fermat coefficients.
• A000975 (program): a(2n) = 2*a(2n-1), a(2n+1) = 2*a(2n)+1 (also a(n) is the n-th number without consecutive equal binary digits).
• A000977 (program): Numbers that are divisible by at least three different primes.
• A000982 (program): a(n) = ceiling(n^2/2).
• A000984 (program): Central binomial coefficients: binomial(2*n,n) = (2*n)!/(n!)^2.
• A000985 (program): Number of n X n symmetric matrices with nonnegative entries and all row sums 2.
• A000986 (program): Number of n X n symmetric matrices with (0,1) entries and all row sums 2.
• A000989 (program): 3-adic valuation of binomial(2*n, n): largest k such that 3^k divides binomial(2*n, n).
• A000990 (program): Number of plane partitions of n with at most two rows.
• A000991 (program): Number of 3-line partitions of n.
• A000994 (program): Shifts 2 places left under binomial transform.
• A000995 (program): Shifts left two terms under the binomial transform.
• A000996 (program): Shifts 3 places left under binomial transform.
• A000997 (program): From a differential equation.
• A000998 (program): From a differential equation.
• A000999 (program): 5-adic valuation of binomial(2*n,n): largest k such that 5^k divides binomial(2*n, n).
• A001000 (program): a(n) = least m such that if a/b < c/d where a,b,c,d are integers in [0,n], then a/b < k/m < c/d for some integer k.
• A001001 (program): Number of sublattices of index n in generic 3-dimensional lattice.
• A001002 (program): Number of dissections of a convex (n+2)-gon into triangles and quadrilaterals by nonintersecting diagonals.
• A001003 (program): Schroeder’s second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.
• A001005 (program): Number of ways of partitioning n points on a circle into subsets only of sizes 2 and 3.
• A001006 (program): Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle.
• A001008 (program): Numerators of harmonic numbers H(n) = Sum_{i=1..n} 1/i.
• A001014 (program): Sixth powers: a(n) = n^6.
• A001015 (program): Seventh powers: a(n) = n^7.
• A001016 (program): Eighth powers: a(n) = n^8.
• A001017 (program): Ninth powers: a(n) = n^9.
• A001018 (program): Powers of 8: a(n) = 8^n.
• A001019 (program): Powers of 9: a(n) = 9^n.
• A001020 (program): Powers of 11: a(n) = 11^n.
• A001021 (program): Powers of 12.
• A001022 (program): Powers of 13.
• A001023 (program): Powers of 14.
• A001024 (program): Powers of 15.
• A001025 (program): Powers of 16: a(n) = 16^n.
• A001026 (program): Powers of 17.
• A001027 (program): Powers of 18.
• A001029 (program): Powers of 19.
• A001030 (program): Fixed under 1 -> 21, 2 -> 211.
• A001031 (program): Goldbach conjecture: a(n) = number of decompositions of 2n into sum of two primes (counting 1 as a prime).
• A001036 (program): Partial sums of A001037, omitting A001037(1).
• A001037 (program): Number of degree-n irreducible polynomials over GF(2); number of n-bead necklaces with beads of 2 colors when turning over is not allowed and with primitive period n; number of binary Lyndon words of length n.
• A001039 (program): a(n) = (p^p-1)/(p-1) where p = prime(n).
• A001040 (program): a(n+1) = n*a(n) + a(n-1) with a(0)=0, a(1)=1.
• A001041 (program): a(0)=12; thereafter a(n) = 12 times the product of the first n primes.
• A001042 (program): a(n) = a(n-1)^2 - a(n-2)^2.
• A001043 (program): Numbers that are the sum of 2 successive primes.
• A001044 (program): a(n) = (n!)^2.
• A001045 (program): Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3.
• A001046 (program): a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = a(1) = 1.
• A001047 (program): a(n) = 3^n - 2^n.
• A001048 (program): a(n) = n! + (n-1)!.
• A001052 (program): a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = 1, a(1) = 2.
• A001053 (program): a(n+1) = n*a(n) + a(n-1) with a(0)=1, a(1)=0.
• A001054 (program): a(n) = a(n-1)*a(n-2) - 1.
• A001056 (program): a(n) = a(n-1)*a(n-2) + 1, a(0) = 1, a(1) = 3.
• A001057 (program): Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.
• A001060 (program): a(n) = a(n-1) + a(n-2) with a(0)=2, a(1)=5. Sometimes called the Evangelist Sequence.
• A001063 (program): E.g.f. satisfies A’(x) = A(x/(1-x)).
• A001064 (program): a(n) = a(n-1)*a(n-2) + a(n-3).
• A001065 (program): Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.
• A001067 (program): Numerator of Bernoulli(2*n)/(2*n).
• A001068 (program): a(n) = floor(5*n/4), numbers that are congruent to {0, 1, 2, 3} mod 5.
• A001069 (program): Log2*(n) (version 2): take log_2 of n this many times to get a number < 2.
• A001075 (program): a(0) = 1, a(1) = 2, a(n) = 4*a(n-1) - a(n-2).
• A001076 (program): Denominators of continued fraction convergents to sqrt(5).
• A001077 (program): Numerators of continued fraction convergents to sqrt(5).
• A001078 (program): a(n) = 10*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.
• A001079 (program): a(n) = 10*a(n-1) - a(n-2); a(0) = 1, a(1) = 5.
• A001080 (program): a(n) = 16*a(n-1) - a(n-2) with a(0) = 0, a(1) = 3.
• A001081 (program): a(n) = 16*a(n-1) - a(n-2).
• A001082 (program): Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, …
• A001084 (program): a(n) = 20*a(n-1) - a(n-2) with a(0) = 0, a(1) = 3.
• A001085 (program): a(n) = 20*a(n-1) - a(n-2).
• A001088 (program): Product of totient function: a(n) = Product_{k=1..n} phi(k) (cf. A000010).
• A001090 (program): a(n) = 8*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
• A001091 (program): a(n) = 8*a(n-1) - a(n-2); a(0) = 1, a(1) = 4.
• A001093 (program): a(n) = n^3 + 1.
• A001094 (program): a(n) = n + n*(n-1)*(n-2)*(n-3).
• A001095 (program): a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4).
• A001096 (program): a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5).
• A001097 (program): Twin primes.
• A001099 (program): a(n) = n^n - a(n-1), with a(1) = 1.
• A001105 (program): a(n) = 2*n^2.
• A001106 (program): 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.
• A001107 (program): 10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).
• A001108 (program): a(n)-th triangular number is a square: a(n+1) = 6*a(n) - a(n-1) + 2, with a(0) = 0, a(1) = 1.
• A001109 (program): a(n)^2 is a triangular number: a(n) = 6*a(n-1) - a(n-2) with a(0)=0, a(1)=1.
• A001110 (program): Square triangular numbers: numbers that are both triangular and square.
• A001112 (program): A continued fraction.
• A001113 (program): Decimal expansion of e.
• A001116 (program): Maximal kissing number of an n-dimensional lattice.
• A001117 (program): a(n) = 3^n - 3*2^n + 3.
• A001118 (program): Differences of 0; labeled ordered partitions into 5 parts.
• A001120 (program): a(0) = a(1) = 1; for n > 1, a(n) = n*a(n-1) + (-1)^n.
• A001122 (program): Primes with primitive root 2.
• A001127 (program): Trajectory of 1 under map x->x + (x-with-digits-reversed).
• A001129 (program): Iccanobif numbers: reverse digits of two previous terms and add.
• A001132 (program): Primes == +-1 (mod 8).
• A001142 (program): a(n) = Product_{k=1..n} k^(2k - 1 - n).
• A001147 (program): Double factorial of odd numbers: a(n) = (2*n-1)!! = 1*3*5*…*(2*n-1).
• A001148 (program): Final digit of 3^n.
• A001156 (program): Number of partitions of n into squares.
• A001157 (program): a(n) = sigma_2(n): sum of squares of divisors of n.
• A001158 (program): sigma_3(n): sum of cubes of divisors of n.
• A001159 (program): sigma_4(n): sum of 4th powers of divisors of n.
• A001160 (program): sigma_5(n), the sum of the 5th powers of the divisors of n.
• A001169 (program): Number of board-pile polyominoes with n cells.
• A001175 (program): Pisano periods (or Pisano numbers): period of Fibonacci numbers mod n.
• A001177 (program): Fibonacci entry points: a(n) = least k >= 1 such that n divides Fibonacci number F_k (=A000045(k)).
• A001182 (program): Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.
• A001189 (program): Number of degree-n permutations of order exactly 2.
• A001193 (program): a(n) = (n+1)*(2*n)!/(2^n*n!) = (n+1)*(2n-1)!!.
• A001194 (program): a(n) = A059366(n,n-2) = A059366(n,2) for n >= 2, where the triangle A059366 arises in the expansion of a trigonometric integral.
• A001196 (program): Double-bitters: only even length runs in binary expansion.
• A001202 (program): a(1)=0, a(2n) = a(n)+1, a(2n+1) = 10*a(n+1).
• A001205 (program): Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.
• A001218 (program): a(n) = 3^n mod 100.
• A001221 (program): Number of distinct primes dividing n (also called omega(n)).
• A001222 (program): Number of prime divisors of n counted with multiplicity (also called big omega of n, bigomega(n) or Omega(n)).
• A001223 (program): Prime gaps: differences between consecutive primes.
• A001224 (program): If F(n) is the n-th Fibonacci number, then a(2n) = (F(2n+1) + F(n+2))/2 and a(2n+1) = (F(2n+2) + F(n+1))/2.
• A001225 (program): Number of consistent arcs in a tournament with n nodes.
• A001226 (program): Lerch’s function q_2(n) = (2^{phi(t)} - 1)/t where t = 2*n - 1.
• A001227 (program): Number of odd divisors of n.
• A001233 (program): Unsigned Stirling numbers of first kind s(n,6).
• A001234 (program): Unsigned Stirling numbers of the first kind s(n,7).
• A001236 (program): Differences of reciprocals of unity.
• A001237 (program): Differences of reciprocals of unity.
• A001238 (program): Differences of reciprocals of unity.
• A001240 (program): Expansion of 1/((1-2x)(1-3x)(1-6x)).
• A001241 (program): Differences of reciprocals of unity.
• A001243 (program): Eulerian numbers (Euler’s triangle: column k=7 of A008292, column k=6 of A173018).
• A001244 (program): Eulerian numbers (Euler’s triangle: column k=8 of A008292, column k=7 of A173018).
• A001246 (program): Squares of Catalan numbers.
• A001247 (program): Squares of Bell numbers.
• A001248 (program): Squares of primes.
• A001249 (program): Squares of tetrahedral numbers: a(n) = binomial(n+3,n)^2.
• A001250 (program): Number of alternating permutations of order n.
• A001254 (program): Squares of Lucas numbers.
• A001255 (program): Squares of partition numbers.
• A001260 (program): Number of permutations of length n with 4 consecutive ascending pairs.
• A001261 (program): Number of permutations of length n with 5 consecutive ascending pairs.
• A001263 (program): Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.
• A001264 (program): Final 2 digits of 4^n.
• A001277 (program): Number of permutations of length n by rises.
• A001278 (program): Number of permutations of length n by rises.
• A001281 (program): Image of n under the map n->n/2 if n even, n->3n-1 if n odd.
• A001283 (program): Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.
• A001284 (program): Numbers of form m*k with m+1 <= k <= 2m-1.
• A001285 (program): Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 1’s and 2’s.
• A001286 (program): Lah numbers: a(n) = (n-1)*n!/2.
• A001287 (program): a(n) = binomial coefficient C(n,10).
• A001288 (program): a(n) = binomial(n,11).
• A001296 (program): 4-dimensional pyramidal numbers: a(n) = (3*n+1)*binomial(n+2, 3)/4. Also Stirling2(n+2, n).
• A001297 (program): Stirling numbers of the second kind S(n+3, n).
• A001298 (program): Stirling numbers of the second kind S(n+4, n).
• A001299 (program): Number of ways of making change for n cents using coins of 1, 5, 10, 25 cents.
• A001300 (program): Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents.
• A001301 (program): Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25 cents.
• A001302 (program): Number of ways of making change for n cents using coins of 1, 2, 5, 10, 25, 50 cents.
• A001303 (program): Stirling numbers of first kind, s(n+3, n), negated.
• A001304 (program): Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)).
• A001305 (program): Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)).
• A001306 (program): Number of ways of making change for n cents using coins of 1, 5, 10, 20, 50, 100 cents.
• A001307 (program): Expansion of 1/(1-x)^2/(1-x^2)/(1-x^4)/(1-x^10)/(1-x^20).
• A001311 (program): Final 2 digits of 6^n.
• A001315 (program): a(n) = Sum_{k=0..n} 2^binomial(n,k).
• A001316 (program): Gould’s sequence: a(n) = Sum_{k=0..n} (binomial(n,k) mod 2); number of odd entries in row n of Pascal’s triangle (A007318); a(n) = 2^A000120(n).
• A001317 (program): Sierpiński’s triangle (Pascal’s triangle mod 2) converted to decimal.
• A001318 (program): Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ….
• A001332 (program): a(n) = Bernoulli(2*n) * (2*n + 1)!.
• A001333 (program): Numerators of continued fraction convergents to sqrt(2).
• A001338 (program): -1 + Sum (k-1)! C(n,k), k = 1..n for n > 0, a(0) = 1.
• A001339 (program): a(n) = Sum_{k=0..n} (k+1)! binomial(n,k).
• A001340 (program): E.g.f.: 2*exp(x)/(1-x)^3.
• A001341 (program): E.g.f.: 6*exp(x)/(1-x)^4;
• A001342 (program): E.g.f.: 24*exp(x)/(1-x)^5.
• A001343 (program): Number of (unordered) ways of making change for n cents using coins of 5, 10, 20, 50, 100 cents.
• A001344 (program): a(n) = sum_{k=0..2} (n+k)! * C(2,k).
• A001345 (program): a(n) = Sum_{k = 0..3} (n+k)! C(3,k).
• A001346 (program): a(n) = Sum_{k = 0..4} (n+k)! C(4,k).
• A001347 (program): a(n) = Sum_{k=0..5} (n+k)! * C(5,k).
• A001348 (program): Mersenne numbers: 2^p - 1, where p is prime.
• A001350 (program): Associated Mersenne numbers.
• A001352 (program): a(0) = 1, a(1) = 6, a(2) = 24; for n>=3, a(n) = 4a(n-1) - a(n-2).
• A001353 (program): a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 1.
• A001354 (program): Coordination sequence for hyperbolic tessellation 3^7 (from triangle group (2,3,7)).
• A001357 (program): Powers of 2 written in base 9.
• A001358 (program): Semiprimes (or biprimes): products of two primes.
• A001359 (program): Lesser of twin primes.
• A001360 (program): Crystal ball sequence for hyperbolic tessellation 3^7 (from triangle group (2,3,7)).
• A001362 (program): Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents.
• A001363 (program): Primes in ternary.
• A001370 (program): Sum of digits of 2^n.
• A001386 (program): Coordination sequence for 4-dimensional I-centered tetragonal orthogonal lattice.
• A001392 (program): a(n) = 9*binomial(2n,n-4)/(n+5).
• A001399 (program): a(n) is the number of partitions of n into at most 3 parts; also partitions of n+3 in which the greatest part is 3; also number of unlabeled multigraphs with 3 nodes and n edges.
• A001400 (program): Number of partitions of n into at most 4 parts.
• A001401 (program): Number of partitions of n into at most 5 parts.
• A001402 (program): Number of partitions of n into at most 6 parts.
• A001405 (program): a(n) = binomial(n, floor(n/2)).
• A001414 (program): Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n).
• A001421 (program): a(n) = (6n)!/((n!)^3*(3n)!).
• A001444 (program): Bending a piece of wire of length n+1 (configurations that can only be brought into coincidence by turning the figure over are counted as different).
• A001445 (program): a(n) = (2^n + 2^[ n/2 ] )/2.
• A001446 (program): a(n) = (4^n + 4^[ n/2 ] )/2.
• A001447 (program): a(n) = (5^n + 5^floor(n/2))/2.
• A001448 (program): a(n) = binomial(4n,2n) or (4*n)!/((2*n)!*(2*n)!).
• A001449 (program): Binomial coefficients binomial(5n,n).
• A001450 (program): a(n) = binomial(5*n,2*n).
• A001451 (program): a(n) = (5*n)!/((3*n)!*n!*n!).
• A001452 (program): Number of 5-line partitions of n.
• A001453 (program): Catalan numbers - 1.
• A001459 (program): a(n) = (5*n)!/((2*n)!*(2*n)!*n!).
• A001460 (program): a(n) = (5*n)!/((2*n)!*(n!)^3).
• A001463 (program): Partial sums of A001462; also a(n) is the last occurrence of n in A001462.
• A001464 (program): E.g.f. exp( -x -(1/2)*x^2 ).
• A001465 (program): Number of degree-n odd permutations of order 2.
• A001468 (program): There are a(n) 2’s between successive 1’s.
• A001469 (program): Genocchi numbers (of first kind); unsigned coefficients give expansion of x*tan(x/2).
• A001470 (program): Number of degree-n permutations of order dividing 3.
• A001471 (program): Number of degree-n permutations of order exactly 3.
• A001472 (program): Number of degree-n permutations of order dividing 4.
• A001475 (program): a(n) = a(n-1) + n * a(n-2), where a(1) = 1, a(2) = 2.
• A001477 (program): The nonnegative integers.
• A001478 (program): The negative integers.
• A001481 (program): Numbers that are the sum of 2 squares.
• A001489 (program): a(n) = -n.
• A001495 (program): Number of symmetric 0-1 (n+1) X (n+1) matrices with row sums 2 and first row starting 1,1 for n > 0, a(0)=1.
• A001497 (program): Triangle of coefficients of Bessel polynomials (exponents in decreasing order).
• A001498 (program): Triangle a(n,k) (n >= 0, 0 <= k <= n) of coefficients of Bessel polynomials y_n(x) (exponents in increasing order).
• A001499 (program): Number of n X n matrices with exactly 2 1’s in each row and column, other entries 0.
• A001504 (program): a(n) = (3*n+1)*(3*n+2).
• A001505 (program): a(n) = (4n+1)(4n+2)(4n+3).
• A001509 (program): (5*n+1)*(5*n+2)*(5*n+3).
• A001511 (program): The ruler function: 2^a(n) divides 2n. Or, a(n) = 2-adic valuation of 2n.
• A001512 (program): a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).
• A001513 (program): a(n) = (6n+1)*(6n+5).
• A001514 (program): Bessel polynomial {y_n}‘(1).
• A001515 (program): Bessel polynomial y_n(x) evaluated at x=1.
• A001516 (program): Bessel polynomial {y_n}’‘(1).
• A001517 (program): Bessel polynomials y_n(x) (see A001498) evaluated at 2.
• A001518 (program): Bessel polynomial y_n(3).
• A001519 (program): a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1.
• A001520 (program): a(n) = (6*n+1)*(6*n+3)*(6*n+5).
• A001521 (program): a(1) = 1; thereafter a(n+1) = floor(sqrt(2*a(n)*(a(n)+1))).
• A001525 (program): a(n) = (3n)!/(3!n!).
• A001526 (program): a(n) = (7n+1)*(7n+6).
• A001527 (program): a(n) = 2 * Sum_{i=0..n} C(2^n-1, i).
• A001533 (program): a(n) = (8n+1)*(8n+7).
• A001534 (program): a(n) = (9n+1)*(9n+8).
• A001535 (program): a(n) = (10n+1)*(10n+9).
• A001536 (program): a(n) = (11n+1)*(11n+10).
• A001538 (program): a(n) = (12n+1)*(12n+11).
• A001539 (program): a(n) = (4*n+1)*(4*n+3).
• A001540 (program): Number of transpositions needed to generate permutations of length n.
• A001541 (program): a(0) = 1, a(1) = 3; for n > 1, a(n) = 6*a(n-1) - a(n-2).
• A001542 (program): a(n) = 6*a(n-1) - a(n-2) for n > 1, a(0)=0 and a(1)=2.
• A001545 (program): a(n) = (5n+1)*(5n+4).
• A001546 (program): a(n) = (8*n+1)*(8*n+3)*(8*n+5)*(8*n+7).
• A001547 (program): a(n) = (7*n+1)*(7*n+2)*(7*n+4).
• A001550 (program): a(n) = 1^n + 2^n + 3^n.
• A001551 (program): a(n) = 1^n + 2^n + 3^n + 4^n.
• A001552 (program): a(n) = 1^n + 2^n + … + 5^n.
• A001553 (program): a(n) = 1^n + 2^n + … + 6^n.
• A001554 (program): a(n) = 1^n + 2^n + … + 7^n.
• A001555 (program): a(n) = 1^n + 2^n + … + 8^n.
• A001556 (program): a(n) = 1^n + 2^n + … + 9^n.
• A001557 (program): a(n) = 1^n + 2^n + … + 10^n.
• A001558 (program): Number of hill-free Dyck paths of semilength n+3 and having length of first descent equal to 1 (a hill in a Dyck path is a peak at level 1).
• A001559 (program): a(0) = 1, a(1) = 4; thereafter a(n)*(2n + 10) - a(n-1)*(11n + 35) + a(n-2)*(8n + 2) + a(n-3)*(15n + 7) + a(n-4)*(4n - 2) = 0.
• A001561 (program): a(n) = (7*n+3)*(7*n+5)*(7*n+6).
• A001563 (program): a(n) = n*n! = (n+1)! - n!.
• A001564 (program): 2nd differences of factorial numbers.
• A001565 (program): 3rd differences of factorial numbers.
• A001570 (program): Numbers k such that k^2 is centered hexagonal.
• A001571 (program): a(n) = 4*a(n-1) - a(n-2) + 1, with a(0) = 0, a(1) = 2.
• A001576 (program): a(n) = 1^n + 2^n + 4^n.
• A001577 (program): An operational recurrence.
• A001579 (program): a(n) = 3^n + 5^n + 6^n.
• A001580 (program): a(n) = 2^n + n^2.
• A001582 (program): Product of Fibonacci and Pell numbers.
• A001584 (program): A generalized Fibonacci sequence.
• A001585 (program): a(n) = 3^n + n^3.
• A001586 (program): Generalized Euler numbers, or Springer numbers.
• A001588 (program): a(n) = a(n-1) + a(n-2) - 1.
• A001589 (program): a(n) = 4^n + n^4.
• A001590 (program): Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=0, a(1)=1, a(2)=0.
• A001591 (program): Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), a(0)=a(1)=a(2)=a(3)=0, a(4)=1.
• A001592 (program): Hexanacci numbers: a(n+1) = a(n)+…+a(n-5) with a(0)=…=a(4)=0, a(5)=1.
• A001593 (program): a(n) = 5^n + n^5.
• A001594 (program): a(n) = 6^n + n^6.
• A001595 (program): a(n) = a(n-1) + a(n-2) + 1, with a(0) = a(1) = 1.
• A001596 (program): a(n) = 7^n + n^7.
• A001602 (program): Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).
• A001603 (program): Odd-indexed terms of A124296.
• A001604 (program): Odd-indexed terms of A124297.
• A001607 (program): a(n) = -a(n-1) - 2*a(n-2).
• A001608 (program): Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.
• A001609 (program): a(1) = a(2) = 1, a(3) = 4; thereafter a(n) = a(n-1) + a(n-3).
• A001610 (program): a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 2.
• A001611 (program): a(n) = Fibonacci(n) + 1.
• A001612 (program): a(n) = a(n-1) + a(n-2) - 1 for n > 1, a(0)=3, a(1)=2.
• A001614 (program): Connell sequence: 1 odd, 2 even, 3 odd, …
• A001615 (program): Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p).
• A001621 (program): a(n) = n*(n + 1)*(n^2 + n + 2)/4.
• A001622 (program): Decimal expansion of golden ratio phi (or tau) = (1 + sqrt(5))/2.
• A001628 (program): Convolved Fibonacci numbers.
• A001629 (program): Self-convolution of Fibonacci numbers.
• A001630 (program): Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=a(1)=0, a(2)=1, a(3)=2.
• A001631 (program): Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with initial conditions a(0..3) = (0, 0, 1, 0).
• A001633 (program): Numbers with an odd number of digits.
• A001634 (program): a(n) = a(n-2) + a(n-3) + a(n-4), with initial values a(0) = 0, a(1) = 2, a(2) = 3, a(3) = 6.
• A001635 (program): A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7.
• A001636 (program): A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8.
• A001637 (program): Numbers with an even number of digits.
• A001638 (program): A Fielder sequence: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
• A001639 (program): A Fielder sequence. a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5), n >= 6.
• A001640 (program): A Fielder sequence.
• A001641 (program): A Fielder sequence: a(n) = a(n-1) + a(n-2) + a(n-4).
• A001642 (program): A Fielder sequence.
• A001643 (program): A Fielder sequence.
• A001644 (program): a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=1, a(2)=3.
• A001645 (program): A Fielder sequence.
• A001648 (program): Tetranacci numbers A073817 without the leading term 4.
• A001649 (program): A Fielder sequence.
• A001650 (program): k appears k times (k odd).
• A001651 (program): Numbers not divisible by 3.
• A001652 (program): a(n) = 6*a(n-1) - a(n-2) + 2 with a(0) = 0, a(1) = 3.
• A001653 (program): Numbers k such that 2*k^2 - 1 is a square.
• A001654 (program): Golden rectangle numbers: F(n)*F(n+1), where F(n) = A000045(n) (Fibonacci numbers).
• A001655 (program): Fibonomial coefficients: a(n) = F(n+1)*F(n+2)*F(n+3)/2, where F() = Fibonacci numbers A000045.
• A001656 (program): Fibonomial coefficients.
• A001657 (program): Fibonomial coefficients: column 5 of A010048.
• A001658 (program): Fibonomial coefficients.
• A001659 (program): Expansion of bracket function.
• A001670 (program): n appears n times (n even).
• A001671 (program): Powers of e rounded up.
• A001680 (program): The partition function G(n,3).
• A001681 (program): The partition function G(n,4).
• A001684 (program): From a continued fraction.
• A001685 (program): a(0) = 1, a(1) = 2, a(2) = 3; for n >= 3, a(n) = a(n-2) + a(n-1)*Product_{i=1..n-3} a(i).
• A001686 (program): From a continued fraction.
• A001687 (program): a(n) = a(n-2) + a(n-5).
• A001688 (program): 4th forward differences of factorial numbers A000142.
• A001689 (program): 5th forward differences of factorial numbers A000142.
• A001690 (program): Non-Fibonacci numbers.
• A001692 (program): Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras.
• A001693 (program): Number of degree-n irreducible polynomials over GF(7); dimensions of free Lie algebras.
• A001694 (program): Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).
• A001696 (program): a(n) = a(n-1)*(1 + a(n-1) - a(n-2)), a(0) = 0, a(1) = 1.
• A001697 (program): a(n+1) = a(n)(a(0) + … + a(n)).
• A001699 (program): Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative.
• A001700 (program): a(n) = binomial(2*n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.
• A001701 (program): Generalized Stirling numbers.
• A001703 (program): Decimal concatenation of n, n+1, and n+2.
• A001704 (program): a(n) = n concatenated with n + 1.
• A001705 (program): Generalized Stirling numbers: a(n) = n! * Sum_{k=0..n-1} (k+1)/(n-k).
• A001706 (program): Generalized Stirling numbers.
• A001707 (program): Generalized Stirling numbers.
• A001708 (program): Generalized Stirling numbers.
• A001709 (program): Generalized Stirling numbers.
• A001710 (program): Order of alternating group A_n, or number of even permutations of n letters.
• A001711 (program): Generalized Stirling numbers.
• A001712 (program): Generalized Stirling numbers.
• A001713 (program): Generalized Stirling numbers.
• A001714 (program): Generalized Stirling numbers.
• A001715 (program): a(n) = n!/6.
• A001716 (program): Generalized Stirling numbers.
• A001717 (program): Generalized Stirling numbers.
• A001718 (program): Generalized Stirling numbers.
• A001719 (program): Generalized Stirling numbers.
• A001720 (program): a(n) = n!/24.
• A001721 (program): Generalized Stirling numbers.
• A001722 (program): Generalized Stirling numbers.
• A001723 (program): Generalized Stirling numbers.
• A001724 (program): Generalized Stirling numbers.
• A001725 (program): a(n) = n!/5!.
• A001729 (program): List of numbers whose digits contain no loops (version 1).
• A001730 (program): a(n) = n!/6!.
• A001735 (program): 5 in base 10-n.
• A001736 (program): 4 in base 10-n.
• A001737 (program): Squares written in base 2.
• A001738 (program): a(n) = n^2 written in base 3.
• A001739 (program): Squares written in base 4.
• A001740 (program): Squares written in base 5.
• A001741 (program): Squares written in base 6.
• A001742 (program): Numbers whose digits contain no loops (version 2).
• A001744 (program): Numbers n such that every digit contains a loop (version 2).
• A001745 (program): Numbers such that at least one digit contains a loop (version 2). Also called “holey” or “holy” numbers.
• A001746 (program): At least one digit contains a loop (version 1).
• A001747 (program): 2 together with primes multiplied by 2.
• A001748 (program): a(n) = 3 * prime(n).
• A001749 (program): Primes multiplied by 4.
• A001750 (program): Primes multiplied by 5.
• A001751 (program): Primes together with primes multiplied by 2.
• A001752 (program): Expansion of 1/((1+x)*(1-x)^5).
• A001753 (program): Expansion of 1/((1+x)*(1-x)^6).
• A001754 (program): Lah numbers: a(n) = n!*binomial(n-1,2)/6.
• A001755 (program): Lah numbers: a(n) = n! * binomial(n-1, 3)/4!.
• A001756 (program): a(n) = A059366(n,n-3) = A059366(n,3) for n >= 3, where the triangle A059366 arises from the expansion of a trigonometric integral.
• A001757 (program): Expansion of an integral: central elements of rows of triangle in A059366.
• A001758 (program): Number of quasi-alternating permutations of length n.
• A001761 (program): a(n) = (2*n)!/(n+1)!.
• A001762 (program): Number of dissections of a ball.
• A001763 (program): Number of dissections of a ball: (3n+3)!/(2n+3)!.
• A001764 (program): a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).
• A001766 (program): Index of (the image of) the modular group Gamma(n) in PSL_2(Z).
• A001768 (program): Sorting numbers: number of comparisons for merge insertion sort of n elements.
• A001769 (program): Expansion of 1/((1+x)*(1-x)^7).
• A001777 (program): Lah numbers: a(n) = n! * binomial(n-1, 4)/5!.
• A001778 (program): Lah numbers: a(n) = n!*binomial(n-1,5)/6!.
• A001779 (program): Expansion of 1/((1+x)(1-x)^8).
• A001780 (program): Expansion of 1/((1+x)(1-x)^9).
• A001781 (program): Expansion of 1/((1+x)*(1-x)^10).
• A001783 (program): n-phi-torial, or phi-torial of n: Product k, 1 <= k <= n, k relatively prime to n.
• A001786 (program): Expansion of 1/((1+x)(1-x)^11).
• A001787 (program): a(n) = n*2^(n-1).
• A001788 (program): a(n) = n*(n+1)*2^(n-2).
• A001789 (program): a(n) = binomial(n,3)*2^(n-3).
• A001790 (program): Numerators in expansion of 1/sqrt(1-x).
• A001791 (program): a(n) = binomial coefficient C(2n, n-1).
• A001792 (program): a(n) = (n+2)*2^(n-1).
• A001793 (program): a(n) = n*(n+3)*2^(n-3).
• A001794 (program): Negated coefficients of Chebyshev T polynomials: x^n, n >= 0.
• A001795 (program): Coefficients of Legendre polynomials.
• A001796 (program): Coefficients of Legendre polynomials.
• A001800 (program): Coefficients of Legendre polynomials.
• A001801 (program): Coefficients of Legendre polynomials.
• A001803 (program): Numerators in expansion of (1 - x)^(-3/2).
• A001804 (program): a(n) = n! * C(n,2).
• A001805 (program): a(n) = n! * binomial(n,3).
• A001806 (program): a(n) = n! * binomial(n,4).
• A001807 (program): a(n) = n! * binomial(n,5).
• A001808 (program): Expansion of 1/((1+x)*(1-x)^12).
• A001809 (program): a(n) = n! * n(n-1)/4.
• A001810 (program): a(n) = n!*n*(n-1)*(n-2)/36.
• A001811 (program): Coefficients of Laguerre polynomials.
• A001812 (program): Coefficients of Laguerre polynomials.
• A001813 (program): Quadruple factorial numbers: a(n) = (2n)!/n!.
• A001814 (program): Coefficient of H_2 when expressing x^{2n} in terms of Hermite polynomials H_m.
• A001815 (program): a(n) = binomial(n,2) * 2^(n-1).
• A001816 (program): Coefficients of x^n in Hermite polynomial H_{n+4}
• A001817 (program): G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).
• A001818 (program): Squares of double factorials: (1*3*5*…*(2n-1))^2 = ((2*n-1)!!)^2.
• A001819 (program): Central factorial numbers: second right-hand column of triangle A008955.
• A001822 (program): Expansion of Sum x^(3n+2)/(1-x^(3n+2)), n=0..inf.
• A001823 (program): Central factorial numbers: column 2 in triangle A008956.
• A001824 (program): Central factorial numbers.
• A001826 (program): Number of divisors of n of the form 4k+1.
• A001831 (program): Number of labeled graded partially ordered sets with n elements of height at most 1.
• A001834 (program): a(0) = 1, a(1) = 5, a(n) = 4*a(n-1) - a(n-2).
• A001835 (program): a(n) = 4*a(n-1) - a(n-2), with a(0) = 1, a(1) = 1.
• A001839 (program): The coding-theoretic function A(n,4,3).
• A001840 (program): Expansion of x /((1 - x)^2 * (1 - x^3)).
• A001841 (program): Related to Zarankiewicz’s problem.
• A001842 (program): Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).
• A001844 (program): Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.
• A001845 (program): Centered octahedral numbers (crystal ball sequence for cubic lattice).
• A001846 (program): Centered 4-dimensional orthoplex numbers (crystal ball sequence for 4-dimensional cubic lattice).
• A001847 (program): Crystal ball sequence for 5-dimensional cubic lattice.
• A001848 (program): Crystal ball sequence for 6-dimensional cubic lattice.
• A001849 (program): Crystal ball sequence for 7-dimensional cubic lattice.
• A001850 (program): Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).
• A001855 (program): Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion.
• A001858 (program): Number of forests of trees on n labeled nodes.
• A001859 (program): Triangular numbers plus quarter-squares: n*(n+1)/2 + floor((n+1)^2/4) (i.e., A000217(n) + A002620(n+1)).
• A001860 (program): Number of series-reduced planted trees with n+9 nodes and 4 internal nodes.
• A001861 (program): Expansion of e.g.f. exp(2*(exp(x) - 1)).
• A001863 (program): Normalized total height of rooted trees with n nodes.
• A001864 (program): Total height of rooted trees with n labeled nodes.
• A001865 (program): Number of connected functions on n labeled nodes.
• A001866 (program): Number of connected graphs with n nodes and n edges.
• A001867 (program): Number of n-bead necklaces with 3 colors.
• A001868 (program): Number of n-bead necklaces with 4 colors.
• A001869 (program): Number of n-bead necklaces with 5 colors.
• A001870 (program): Expansion of (1-x)/(1 - 3*x + x^2)^2.
• A001871 (program): Expansion of 1/(1 - 3*x + x^2)^2.
• A001872 (program): Convolved Fibonacci numbers.
• A001873 (program): Convolved Fibonacci numbers.
• A001874 (program): Convolved Fibonacci numbers.
• A001875 (program): Convolved Fibonacci numbers.
• A001876 (program): Number of divisors of n of form 5k+1; a(0)=0.
• A001877 (program): Number of divisors of n of the form 5k+2; a(0) = 0.
• A001878 (program): Number of divisors of n of form 5k+3; a(0) = 0.
• A001879 (program): a(n) = (2n+2)!/(n!*2^(n+1)).
• A001880 (program): Coefficients of Bessel polynomials y_n (x).
• A001881 (program): Coefficients of Bessel polynomials y_n (x).
• A001882 (program): a(2n) = a(2n-1) + 2a(2n-2), a(2n+1) = a(2n) + a(2n-1), with a(1) = 2 and a(2) = 3.
• A001891 (program): Hit polynomials; convolution of natural numbers with Fibonacci numbers F(2), F(3), F(4), ….
• A001892 (program): Number of permutations of (1,…,n) having n-2 inversions (n>=2).
• A001893 (program): Number of permutations of (1,…,n) having n-3 inversions (n>=3).
• A001894 (program): Number of permutations of {1,…,n} having n-4 inversions (n>=4).
• A001896 (program): Numerators of cosecant numbers -2*(2^(2*n - 1) - 1)*Bernoulli(2*n); also of Bernoulli(2*n, 1/2) and Bernoulli(2*n, 1/4).
• A001897 (program): Denominators of cosecant numbers: -2*(2^(2*n-1)-1)*Bernoulli(2*n).
• A001898 (program): Denominators of Bernoulli polynomials B(n)(x).
• A001899 (program): Number of divisors of n of form 5k+4; a(0) = 0.
• A001900 (program): Successive numerators of Wallis’s approximation to Pi/2 (unreduced).
• A001901 (program): Successive numerators of Wallis’s approximation to Pi/2 (reduced).
• A001902 (program): Successive denominators of Wallis’s approximation to Pi/2 (reduced).
• A001903 (program): Final digit of 7^n.
• A001906 (program): F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).
• A001907 (program): Expansion of e.g.f. exp(-x)/(1-4*x).
• A001908 (program): E.g.f. exp(-x)/(1-5*x).
• A001909 (program): a(n) = n*a(n-1) + (n-4)*a(n-2), a(2) = 0, a(3) = 1.
• A001910 (program): a(n) = n*a(n-1) + (n-5)*a(n-2).
• A001911 (program): a(n) = Fibonacci(n+3) - 2.
• A001912 (program): Numbers k such that 4*k^2 + 1 is prime.
• A001917 (program): (p-1)/x, where p = prime(n) and x = ord(2,p), the smallest positive integer such that 2^x == 1 mod p.
• A001919 (program): Eighth column of quadrinomial coefficients.
• A001921 (program): a(n) = 14*a(n-1) - a(n-2) + 6 for n>1, a(0)=0, a(1)=7.
• A001922 (program): Numbers k such that 3*k^2 - 3*k + 1 is both a square (A000290) and a centered hexagonal number (A003215).
• A001923 (program): a(n) = Sum_{k=1..n} k^k.
• A001924 (program): Apply partial sum operator twice to Fibonacci numbers.
• A001925 (program): From rook polynomials.
• A001926 (program): G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].
• A001932 (program): Sum of Fibonacci (A000045) and Pell (A000129) numbers.
• A001934 (program): Expansion of 1/theta_4(q)^2 in powers of q.
• A001935 (program): Number of partitions with no even part repeated; partitions of n in which no parts are multiples of 4.
• A001936 (program): Expansion of q^(-1/4) * (eta(q^4) / eta(q))^2 in powers of q.
• A001937 (program): Expansion of (psi(x^2) / psi(-x))^3 in powers of x where psi() is a Ramanujan theta function.
• A001938 (program): Expansion of k/(4*q^(1/2)) in powers of q, where k defined by sqrt(k) = theta_2(0, q))/theta_3(0, q).
• A001939 (program): Expansion of (psi(-x) / phi(-x))^5 in powers of x where phi(), psi() are Ramanujan theta functions.
• A001940 (program): Absolute value of coefficients of an elliptic function.
• A001941 (program): Absolute values of coefficients of an elliptic function.
• A001943 (program): Expansion of reciprocal of theta series of E_8 lattice.
• A001945 (program): a(n+6) = -a(n+5) + a(n+4) + 3a(n+3) + a(n+2) - a(n+1) - a(n). a(n) = sign(n) if abs(n)<=3.
• A001946 (program): a(n) = 11*a(n-1) + a(n-2).
• A001947 (program): a(n) = Lucas(5*n+2).
• A001949 (program): Solutions of a fifth-order probability difference equation.
• A001950 (program): Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2.
• A001951 (program): A Beatty sequence: a(n) = floor(n*sqrt(2)).
• A001952 (program): A Beatty sequence: a(n) = floor(n*(2 + sqrt(2))).
• A001953 (program): a(n) = floor((n + 1/2) * sqrt(2)).
• A001954 (program): a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff game.
• A001955 (program): Beatty sequence of 1 + 1/sqrt(11).
• A001956 (program): Beatty sequence of (5+sqrt(13))/2.
• A001957 (program): u-pile positions in the 3-Wythoff game with i=1.
• A001958 (program): v-pile numbers of the 3-Wythoff game with i=1.
• A001959 (program): u-pile numbers for the 3-Wythoff game with i=2.
• A001960 (program): a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.
• A001961 (program): A Beatty sequence: floor(n * (sqrt(5) - 1)).
• A001962 (program): A Beatty sequence: floor(n * (sqrt(5) + 3)).
• A001963 (program): Winning positions in the u-pile of the 4-Wythoff game with i=1.
• A001964 (program): v-pile positions of the 4-Wythoff game with i=1.
• A001965 (program): u-pile count for the 4-Wythoff game with i=2.
• A001966 (program): v-pile counts for the 4-Wythoff game with i=2.
• A001967 (program): u-pile positions for the 4-Wythoff game with i=3.
• A001968 (program): v-pile positions of the 4-Wythoff game with i=3.
• A001969 (program): Evil numbers: nonnegative integers with an even number of 1’s in their binary expansion.
• A001971 (program): Nearest integer to n^2/8.
• A001972 (program): Expansion of 1/((1-x)^2*(1-x^4)) = 1/( (1+x)*(1+x^2)*(1-x)^3 ).
• A001973 (program): Expansion of (1+x^3)/((1-x)*(1-x^2)^2*(1-x^3)).
• A001983 (program): Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.
• A001993 (program): Number of two-rowed partitions of length 3.
• A001994 (program): Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).
• A001996 (program): Number of partitions of n into parts 2, 3, 4, 5, 6, 7.
• A001998 (program): Bending a piece of wire of length n+1; walks of length n+1 on a tetrahedron; also non-branched catafusenes with n+2 condensed hexagons.
• A002001 (program): a(n) = 3*4^(n-1), n>0; a(0)=1.
• A002002 (program): a(n) = Sum_{k=0..n-1} binomial(n,k+1) * binomial(n+k,k).
• A002003 (program): a(n) = 2 * Sum_{k=0..n-1} binomial(n-1, k)*binomial(n+k, k).
• A002004 (program): Davenport-Schinzel numbers of degree 4 on n symbols.
• A002005 (program): Number of rooted planar cubic maps with 2n vertices.
• A002011 (program): a(n) = 4*(2n+1)!/n!^2.
• A002015 (program): a(n) = n^2 reduced mod 100.
• A002016 (program): Number of first n tetrahedral numbers (A000292) that are relatively prime to n.
• A002018 (program): From a distribution problem.
• A002019 (program): a(n) = a(n-1) - (n-1)(n-2)a(n-2).
• A002020 (program): a(n+1) = a(n) - n*(n-1)*a(n-1), with a(n) = 1 for n <= 3.
• A002021 (program): Pile of coconuts problem: (n-1)(n^n - 1), n even; n^n - n + 1, n odd.
• A002022 (program): Pile of coconuts problem.
• A002023 (program): a(n) = 6*4^n.
• A002024 (program): k appears k times; a(n) = floor(sqrt(2n) + 1/2).
• A002026 (program): Generalized ballot numbers (first differences of Motzkin numbers).
• A002033 (program): Number of perfect partitions of n.
• A002034 (program): Kempner numbers: smallest positive integer m such that n divides m!.
• A002035 (program): Numbers that contain primes to odd powers only.
• A002039 (program): Convolution inverse of A143348.
• A002041 (program): Expansion of x/((1-x)(1-4x^2)(1-5x)).
• A002042 (program): a(n) = 7*4^n.
• A002050 (program): Number of simplices in barycentric subdivision of n-simplex.
• A002051 (program): Steffensen’s bracket function [n,2].
• A002053 (program): a(n) = least value of m for which Liouville’s function A002819(m) = -n.
• A002054 (program): Binomial coefficient C(2n+1, n-1).
• A002055 (program): Number of diagonal dissections of a convex n-gon into n-4 regions.
• A002056 (program): Number of diagonal dissections of a convex n-gon into n-5 regions.
• A002057 (program): Fourth convolution of Catalan numbers: 4*binomial(2n+3,n)/(n+4).
• A002058 (program): Number of internal triangles in all triangulations of an (n+1)-gon.
• A002059 (program): Number of partitions of an n-gon into (n-4) parts.
• A002060 (program): Number of partitions of an n-gon into (n-5) parts.
• A002061 (program): Central polygonal numbers: a(n) = n^2 - n + 1.
• A002062 (program): a(n) = Fibonacci(n) + n.
• A002063 (program): a(n) = 9*4^n.
• A002064 (program): Cullen numbers: a(n) = n*2^n + 1.
• A002065 (program): a(n+1) = a(n)^2 + a(n) + 1.
• A002066 (program): a(n) = 10*4^n.
• A002081 (program): Numbers congruent to {2, 4, 8, 16} (mod 20).
• A002082 (program): 2nd differences are periodic.
• A002083 (program): Narayana-Zidek-Capell numbers: a(n) = 1 for n <= 2. Otherwise a(2n) = 2a(2n-1), a(2n+1) = 2a(2n) - a(n).
• A002084 (program): Sinh x / cos x = Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)!.
• A002085 (program): From the expansion of sinh x / cos x: a(n) = odd part of A002084(n).
• A002088 (program): Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010.
• A002089 (program): a(n) = 11*4^n.
• A002095 (program): Number of partitions of n into nonprime parts.
• A002102 (program): Number of nonnegative solutions to x^2 + y^2 + z^2 = n.
• A002104 (program): Logarithmic numbers.
• A002105 (program): Reduced tangent numbers: 2^n*(2^{2n} - 1)*|B_{2n}|/n, where B_n = Bernoulli numbers.
• A002107 (program): Expansion of Product_{k>=1} (1 - x^k)^2.
• A002108 (program): 4th powers written backwards.
• A002109 (program): Hyperfactorials: Product_{k = 1..n} k^k.
• A002110 (program): Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.
• A002112 (program): Glaisher’s H numbers.
• A002113 (program): Palindromes in base 10.
• A002114 (program): Glaisher’s H’ numbers.
• A002117 (program): Decimal expansion of zeta(3) = Sum_{m >= 1} 1/m^3.
• A002118 (program): 5th powers written backwards.
• A002119 (program): Bessel polynomial y_n(-2).
• A002120 (program): a(1) = 0, a(2) = -2; for n > 2, a(n) + a(n-2) - a(n-3) - a(n-5) - … - a(n-p) = (-1)^(n+1)*n if n is prime, otherwise = 0, where p = largest prime < n.
• A002121 (program): a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p).
• A002123 (program): a(1) = 0, a(2) = 0; for n > 2, a(n) - a(n-3) - a(n-5) - … - a(n-p) = n if n is prime, otherwise = 0, where p = largest prime < n.
• A002124 (program): Number of compositions of n into a sum of odd primes.
• A002129 (program): Generalized sum of divisors function: excess of sum of odd divisors of n over sum of even divisors of n.
• A002131 (program): Sum of divisors d of n such that n/d is odd.
• A002133 (program): Number of partitions of n with exactly two part sizes.
• A002135 (program): Number of terms in a symmetrical determinant: a(n) = n*a(n-1) - (n-1)*(n-2)*a(n-3)/2.
• A002136 (program): Matrices with 2 rows.
• A002137 (program): Number of n X n symmetric matrices with nonnegative integer entries, trace 0 and all row sums 2.
• A002138 (program): 6th powers written backwards.
• A002140 (program): 7th powers written backwards.
• A002143 (program): Class numbers h(-p) where p runs through the primes p == 3 (mod 4).
• A002144 (program): Pythagorean primes: primes of form 4*k + 1.
• A002145 (program): Primes of the form 4*k + 3.
• A002161 (program): Decimal expansion of square root of Pi.
• A002162 (program): Decimal expansion of the natural logarithm of 2.
• A002163 (program): Decimal expansion of square root of 5.
• A002171 (program): Glaisher’s chi numbers. a(n) = chi(4*n + 1).
• A002173 (program): a(n) = Sum_{d|n, d == 1 mod 4} d^2 - Sum_{d|n, d == 3 mod 4} d^2.
• A002175 (program): Excess of number of divisors of 12n+1 of form 4k+1 over those of form 4k+3.
• A002191 (program): Possible values for sum of divisors of n.
• A002193 (program): Decimal expansion of square root of 2.
• A002194 (program): Decimal expansion of sqrt(3).
• A002203 (program): Companion Pell numbers: a(n) = 2*a(n-1) + a(n-2), a(0) = a(1) = 2.
• A002204 (program): An ill-conditioned determinant.
• A002212 (program): Number of restricted hexagonal polyominoes with n cells.
• A002217 (program): Starting with n, repeatedly calculate the sum of prime factors (with repetition) of the previous term, until reaching 0 or a fixed point: a(n) is the number of terms in the resulting sequence.
• A002232 (program): 8th powers written backwards.
• A002239 (program): 9th powers written backwards.
• A002241 (program): 10th powers written backwards.
• A002246 (program): a(1) = 3; for n > 1, a(n) = 4*phi(n); given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.
• A002247 (program): A (6,2)-sequence.
• A002248 (program): Number of points on y^2 + xy = x^3 + x^2 + x over GF(2^n).
• A002249 (program): a(n) = a(n-1) - 2*a(n-2) with a(0) = 2, a(1) = 1.
• A002250 (program): a(n) = 4^n - 2*3^n.
• A002251 (program): Start with the nonnegative integers; then swap L(k) and U(k) for all k >= 1, where L = A000201, U = A001950 (lower and upper Wythoff sequences).
• A002260 (program): Triangle read by rows: T(n,k) = k for n >= 1, k = 1..n.
• A002262 (program): Triangle read by rows: T(n,k), 0 <= k <= n, in which row n lists the first n+1 nonnegative integers.
• A002264 (program): Nonnegative integers repeated 3 times.
• A002265 (program): Nonnegative integers repeated 4 times.
• A002266 (program): Integers repeated 5 times.
• A002267 (program): The 15 supersingular primes: primes dividing order of Monster simple group.
• A002271 (program): All odd numbers k, 1 < k < n, relatively prime to n are primes.
• A002275 (program): Repunits: (10^n - 1)/9. Often denoted by R_n.
• A002276 (program): a(n) = 2*(10^n - 1)/9.
• A002277 (program): a(n) = 3*(10^n - 1)/9.
• A002278 (program): a(n) = 4*(10^n - 1)/9.
• A002279 (program): a(n) = 5*(10^n - 1)/9.
• A002280 (program): a(n) = 6*(10^n - 1)/9.
• A002281 (program): a(n) = 7(10^n - 1)/9.
• A002282 (program): a(n) = 8*(10^n - 1)/9.
• A002283 (program): a(n) = 10^n - 1.
• A002288 (program): G.f.: q * Product_{m>=1} (1-q^m)^8*(1-q^2m)^8.
• A002293 (program): Number of dissections of a polygon: binomial(4*n, n)/(3*n + 1).
• A002294 (program): a(n) = binomial(5*n, n)/(4*n + 1).
• A002295 (program): Number of dissections of a polygon: binomial(6n,n)/(5n+1).
• A002296 (program): Number of dissections of a polygon: binomial(7n,n)/(6n+1).
• A002297 (program): Numerator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
• A002298 (program): Denominator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
• A002299 (program): Binomial coefficients C(2*n+5,5).
• A002301 (program): a(n) = n! / 3.
• A002302 (program): Generalized tangent numbers.
• A002309 (program): Sum of first n fourth powers of odd numbers.
• A002310 (program): a(n) = 5*a(n-1) - a(n-2).
• A002312 (program): Arc-cotangent reducible numbers or non-Størmer numbers: largest prime factor of k^2 + 1 is less than 2*k.
• A002313 (program): Primes congruent to 1 or 2 modulo 4; or, primes of form x^2 + y^2; or, -1 is a square mod p.
• A002314 (program): Minimal integer square root of -1 modulo p, where p is the n-th prime of the form 4k+1.
• A002315 (program): NSW numbers: a(n) = 6*a(n-1) - a(n-2); also a(n)^2 - 2*b(n)^2 = -1 with b(n) = A001653(n+1).
• A002316 (program): Related to Bernoulli numbers.
• A002317 (program): Related to Genocchi numbers.
• A002318 (program): Expansion of (1/theta_4(q)^2 -1)/4 in powers of q.
• A002320 (program): a(n) = 5*a(n-1) - a(n-2).
• A002321 (program): Mertens’s function: Sum_{k=1..n} mu(k), where mu is the Moebius function A008683.
• A002323 (program): ((2^m - 1) / p) mod p, where p = prime(n) and m = ord(2,p).
• A002324 (program): Number of divisors of n == 1 (mod 3) minus number of divisors of n == 2 (mod 3).
• A002325 (program): Glaisher’s J numbers.
• A002326 (program): Multiplicative order of 2 mod 2n+1.
• A002327 (program): Primes of the form k^2 - k - 1.
• A002328 (program): Numbers n such that n^2 - n - 1 is prime.
• A002329 (program): Periods of reciprocals of integers prime to 10.
• A002348 (program): Degree of rational Poncelet porism of n-gon.
• A002370 (program): a(n) = (2*n-1)^2 * a(n-1) - 3*C(2*n-1,3) * a(n-2) for n>1; a(0) = a(1) = 1.
• A002371 (program): Period of decimal expansion of 1/(n-th prime) (0 by convention for the primes 2 and 5).
• A002372 (program): Goldbach conjecture: number of decompositions of 2n into ordered sums of two odd primes.
• A002373 (program): Smallest prime in decomposition of 2n into sum of two odd primes.
• A002374 (program): Largest prime <= n in any decomposition of 2n into a sum of two odd primes.
• A002375 (program): From Goldbach conjecture: number of decompositions of 2n into an unordered sum of two odd primes.
• A002378 (program): Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
• A002379 (program): a(n) = floor(3^n / 2^n).
• A002380 (program): a(n) = 3^n reduced modulo 2^n.
• A002381 (program): Numbers of the form (p^2 - 1)/120 where p is 1 or prime.
• A002382 (program): Numbers of the form (p^2 - 49)/120 where p is prime.
• A002383 (program): Primes of form k^2 + k + 1.
• A002384 (program): Numbers n such that n^2 + n + 1 is prime.
• A002388 (program): Decimal expansion of Pi^2.
• A002390 (program): Decimal expansion of natural logarithm of golden ratio.
• A002391 (program): Decimal expansion of natural logarithm of 3.
• A002397 (program): a(n) = n! * lcm({1, 2, .. n + 1}).
• A002407 (program): Cuban primes: primes which are the difference of two consecutive cubes.
• A002408 (program): Expansion of 8-dimensional cusp form.
• A002409 (program): a(n) = 2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.
• A002411 (program): Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.
• A002412 (program): Hexagonal pyramidal numbers, or greengrocer’s numbers.
• A002413 (program): Heptagonal (or 7-gonal) pyramidal numbers: a(n) = n*(n+1)*(5*n-2)/6.
• A002414 (program): Octagonal pyramidal numbers: a(n) = n*(n+1)*(2*n-1)/2.
• A002415 (program): 4-dimensional pyramidal numbers: a(n) = n^2*(n^2-1)/12.
• A002416 (program): a(n) = 2^(n^2).
• A002417 (program): 4-dimensional figurate numbers: a(n) = n*binomial(n+2, 3).
• A002418 (program): 4-dimensional figurate numbers: a(n) = (5*n-1)*binomial(n+2,3)/4.
• A002419 (program): 4-dimensional figurate numbers: a(n) = (6*n-2)*binomial(n+2,3)/4.
• A002420 (program): Expansion of sqrt(1 - 4*x) in powers of x.
• A002421 (program): Expansion of (1-4*x)^(3/2) in powers of x.
• A002422 (program): Expansion of (1-4*x)^(5/2).
• A002423 (program): Expansion of (1-4*x)^(7/2).
• A002424 (program): Expansion of (1-4*x)^(9/2).
• A002425 (program): Denominator of Pi^(2n)/(Gamma(2n)*(1-2^(-2n))*zeta(2n)).
• A002426 (program): Central trinomial coefficients: largest coefficient of (1 + x + x^2)^n.
• A002427 (program): Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
• A002428 (program): Numerators of coefficients of expansion of arctan(x)^2 = x^2 - 2/3*x^4 + 23/45*x^6 - 44/105*x^8 + 563/1575*x^10 - 3254/10395*x^12 + …
• A002430 (program): Numerators in Taylor series for tan(x). Also from Taylor series for tanh(x).
• A002431 (program): Numerators in Taylor series for cot x.
• A002436 (program): E.g.f.: Sum_{n >= 0} a(n)*x^(2*n)/(2*n)! = sec(2*x).
• A002437 (program): a(n) = A000364(n) * (3^(2*n+1) + 1)/4.
• A002438 (program): Multiples of Euler numbers.
• A002440 (program): Squares written in base 7.
• A002441 (program): Squares written in base 8.
• A002442 (program): Squares written in base 9.
• A002444 (program): Denominator in Feinler’s formula for unsigned Bernoulli number |B_{2n}|.
• A002445 (program): Denominators of Bernoulli numbers B_{2n}.
• A002446 (program): a(n) = 2^(2*n+1) - 2.
• A002447 (program): Expansion of 1/(1-2*x^2-3*x^3).
• A002448 (program): Expansion of Jacobi theta function theta_4(x).
• A002450 (program): a(n) = (4^n - 1)/3.
• A002451 (program): Expansion of 1/((1-x)*(1-4*x)*(1-9*x)).
• A002452 (program): a(n) = (9^n - 1)/8.
• A002453 (program): Central factorial numbers.
• A002454 (program): Central factorial numbers: a(n) = 4^n (n!)^2.
• A002455 (program): Central factorial numbers.
• A002456 (program): Joffe’s central differences of 0, A241171(n,n-1).
• A002457 (program): a(n) = (2n+1)!/n!^2.
• A002458 (program): a(n) = binomial(4*n+1, 2*n).
• A002459 (program): Nearest integer to cosh(n).
• A002461 (program): Coefficients of Legendre polynomials.
• A002462 (program): Coefficients of Legendre polynomials.
• A002463 (program): Coefficients of Legendre polynomials.
• A002467 (program): The game of Mousetrap with n cards (given n letters and n envelopes, how many ways are there to fill the envelopes so that at least one letter goes into its right envelope?).
• A002469 (program): The game of Mousetrap with n cards: the number of permutations of n cards in which 2 is the only hit.
• A002471 (program): Number of partitions of n into a prime and a square.
• A002472 (program): Number of pairs x,y such that y-x=2, (x,n)=1, (y,n)=1 and 1 <= x <= n.
• A002473 (program): 7-smooth numbers: positive numbers whose prime divisors are all <= 7.
• A002474 (program): Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).
• A002476 (program): Primes of the form 6m + 1.
• A002477 (program): Wonderful Demlo numbers: a(n) = ((10^n - 1)/9)^2.
• A002478 (program): Bisection of A000930.
• A002479 (program): Numbers of form x^2 + 2y^2.
• A002480 (program): Numbers of form 2x^2 + 3y^2.
• A002481 (program): Numbers of form x^2 + 6y^2.
• A002483 (program): Expansion of Jacobi theta function {theta_1}‘(q) in powers of q^(1/4).
• A002487 (program): Stern’s diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2*n) = a(n), a(2*n+1) = a(n) + a(n+1).
• A002489 (program): a(n) = n^(n^2), or (n^n)^n.
• A002491 (program): Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire that make use of n-th hole.
• A002492 (program): Sum of the first n even squares: 2*n*(n+1)*(2*n+1)/3.
• A002496 (program): Primes of the form k^2 + 1.
• A002501 (program): a(n) = 7^n - 3*4^n + 2*3^n.
• A002503 (program): Numbers k such that binomial(2*k,k) is divisible by (k+1)^2.
• A002504 (program): Numbers x such that 1 + 3x*(x-1) is a (“cuban”) prime (cf. A002407).
• A002506 (program): Denominators of coefficients of expansion of Bessel function J_2(x).
• A002513 (program): Number of “cubic partitions” of n: expansion of Product_{k>0} 1/((1-x^(2k))^2*(1-x^(2k-1))) in powers of x.
• A002515 (program): Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
• A002522 (program): a(n) = n^2 + 1.
• A002523 (program): a(n) = n^4 + 1.
• A002524 (program): Number of permutations of length n within distance 2 of a fixed permutation.
• A002525 (program): Number of permutations according to distance.
• A002530 (program): a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.
• A002531 (program): a(2*n) = a(2*n-1) + a(2*n-2), a(2*n+1) = 2*a(2*n) + a(2*n-1); a(0) = a(1) = 1.
• A002532 (program): a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 0, a(1) = 1.
• A002533 (program): a(n) = 2*a(n-1) + 5*a(n-2).
• A002534 (program): a(n) = 2*a(n-1) + 9*a(n-2).
• A002535 (program): a(n) = 2*a(n-1) + 9*a(n-2), with a(0)=a(1)=1.
• A002536 (program): a(n) = 8 a(n-2) - 9 a(n-4).
• A002537 (program): a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).
• A002538 (program): Second-order Eulerian numbers «n+1,n-1».
• A002541 (program): a(n) = Sum_{k=1..n-1} floor((n-k)/k).
• A002544 (program): a(n) = binomial(2*n+1,n)*(n+1)^2.
• A002547 (program): Numerator of the n-th harmonic number H(n) divided by (n+1); a(n) = A001008(n) / ((n+1)*A002805(n)).
• A002548 (program): Denominators of coefficients for numerical differentiation.
• A002549 (program): Numerators of coefficients of log(1+x)/sqrt(1+x).
• A002550 (program): Denominators of coefficients of log(1+x)/sqrt(1+x).
• A002553 (program): Coefficients for numerical differentiation.
• A002554 (program): Numerators of coefficients for numerical differentiation.
• A002555 (program): Denominators of coefficients for numerical differentiation.
• A002561 (program): a(n) = n^5 + 1.
• A002570 (program): From a definite integral.
• A002571 (program): From a definite integral.
• A002578 (program): Number of integral points in a certain sequence of open quadrilaterals.
• A002579 (program): Number of integral points in a certain sequence of closed quadrilaterals.
• A002580 (program): Decimal expansion of cube root of 2.
• A002581 (program): Decimal expansion of cube root of 3.
• A002586 (program): Smallest prime factor of 2^n + 1.
• A002593 (program): a(n) = n^2*(2*n^2 - 1); also Sum_{k=0..n-1} (2k+1)^3.
• A002594 (program): a(n) = n^2*(16*n^4-20*n^2+7)/3.
• A002595 (program): Denominators of Taylor series expansion of arcsin(x). Also arises from arccos(x), arccsc(x), arcsec(x), arcsinh(x).
• A002596 (program): Numerators in expansion of sqrt(1+x). Absolute values give numerators in expansion of sqrt(1-x).
• A002597 (program): Number of partitions into one kind of 1’s, two kinds of 2’s, and three kinds of 3’s.
• A002604 (program): a(n) = n^6 + 1.
• A002605 (program): a(n) = 2*(a(n-1) + a(n-2)), a(0) = 0, a(1) = 1.
• A002618 (program): a(n) = n*phi(n).
• A002620 (program): Quarter-squares: a(n) = floor(n/2)*ceiling(n/2). Equivalently, a(n) = floor(n^2/4).
• A002621 (program): Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
• A002622 (program): Number of partitions of at most n into at most 5 parts.
• A002623 (program): Expansion of 1/((1-x)^4*(1+x)).
• A002624 (program): Expansion of (1-x)^(-3) * (1-x^2)^(-2).
• A002625 (program): Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
• A002626 (program): Expansion of 1/((1-x)^3 (1-x^2)^2 (1-x^3) (1-x^4)).
• A002627 (program): a(n) = n*a(n-1) + 1, a(0) = 0.
• A002628 (program): Number of permutations of length n without 3-sequences.
• A002629 (program): Number of permutations of length n with one 3-sequence.
• A002630 (program): Number of permutations of length n with two 3-sequences.
• A002633 (program): Related to discordant permutations.
• A002640 (program): Numbers n such that (n^2 + n + 1)/3 is prime.
• A002648 (program): A variant of the cuban primes: primes p = (x^3 - y^3 )/(x - y) where x = y + 2.
• A002652 (program): Theta series of Kleinian lattice Z[(1 + sqrt(-7))/ 2] in 1 complex (or 2 real) dimensions.
• A002654 (program): Number of ways of writing n as a sum of at most two nonzero squares, where order matters; also (number of divisors of n of form 4m+1) - (number of divisors of form 4m+3).
• A002658 (program): a(0) = a(1) = 1; for n > 0, a(n+1) = a(n)*(a(0) + … + a(n-1)) + a(n)*(a(n) + 1)/2.
• A002659 (program): a(n) = 2*sigma(n) - 1.
• A002660 (program): a(n) = Sum_{d|n, d <= 3} d^2 + 3*Sum_{d|n, d>3} d.
• A002661 (program): Least integer having Radon random number n.
• A002662 (program): a(n) = 2^n - 1 - n*(n+1)/2.
• A002663 (program): a(n) = 2^n - C(n,0) - C(n,1) - C(n,2) - C(n,3).
• A002664 (program): a(n) = 2^n - C(n,0)- … - C(n,4).
• A002665 (program): Continued fraction expansion of Lehmer’s constant.
• A002671 (program): a(n) = 4^n*(2*n+1)!.
• A002672 (program): Denominators of central difference coefficients M_{3}^(2n+1).
• A002673 (program): Numerators of central difference coefficients M_{3}^(2n+1).
• A002674 (program): a(n) = (2n)!/2.
• A002675 (program): Numerators of coefficients for central differences M_{4}^(2*n).
• A002676 (program): Denominators of coefficients for central differences M_{4}^(2*n).
• A002677 (program): Denominators of coefficients for central differences M_{3}’^(2*n+1).
• A002678 (program): Numerators of the Taylor coefficients of (e^x-1)^2.
• A002679 (program): Denominator of 2*Stirling_2(n,2)/n!.
• A002690 (program): a(n) = (n+1) * (2*n)! / n!.
• A002691 (program): a(n) = (n+2) * (2n+1) * (2n-1)! / (n-1)!.
• A002694 (program): Binomial coefficients C(2n, n-2).
• A002695 (program): P_n’(3), where P_n is n-th Legendre polynomial.
• A002696 (program): Binomial coefficients C(2n,n-3).
• A002697 (program): a(n) = n*4^(n-1).
• A002698 (program): Coefficients of Chebyshev polynomials: n(2n-3)2^(2n-5).
• A002699 (program): a(n) = n*2^(2*n-1).
• A002700 (program): Coefficients of Chebyshev polynomials: n*(2*n+1) * 4^(n-1).
• A002701 (program): Coefficients for numerical differentiation.
• A002704 (program): Number of sets with a congruence property.
• A002705 (program): Sets with a congruence property.
• A002708 (program): a(n) = Fibonacci(n) mod n.
• A002714 (program): Number of different keys with n cuts, depths between 1 and 7 and depth difference at most 1 between adjacent cut depths.
• A002715 (program): An infinite coprime sequence defined by recursion.
• A002716 (program): An infinite coprime sequence defined by recursion.
• A002717 (program): a(n) = floor(n(n+2)(2n+1)/8).
• A002720 (program): Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column.
• A002726 (program): a(n) = Fibonacci(n+1) mod n.
• A002727 (program): Number of 3 X n binary matrices up to row and column permutations.
• A002731 (program): Numbers n such that (n^2 + 1)/2 is prime.
• A002732 (program): Numbers n such that (4n^2 + 1)/5 is prime.
• A002733 (program): Numbers k such that (k^2 + 1)/10 is prime.
• A002734 (program): Remove squares!
• A002736 (program): Apéry numbers: a(n) = n^2*C(2n,n).
• A002737 (program): a(n) = Sum_{j=0..n} (n+j)*binomial(n+j,j).
• A002738 (program): Coefficients for extrapolation.
• A002739 (program): a(n) = ((2*n-1)!/(2*n!*(n-2)!))*((n^3-3*n^2+2*n+2)/(n^2-1)).
• A002740 (program): Number of tree-rooted bridgeless planar maps with two vertices and n faces.
• A002741 (program): Logarithmic numbers: expansion of the e.g.f. -log(1-x) * e^(-x).
• A002742 (program): Logarithmic numbers.
• A002743 (program): Sum of logarithmic numbers.
• A002744 (program): Sum of logarithmic numbers.
• A002745 (program): Sum of logarithmic numbers.
• A002746 (program): Sum of logarithmic numbers.
• A002747 (program): Logarithmic numbers.
• A002748 (program): Sum of logarithmic numbers.
• A002749 (program): Sum of logarithmic numbers.
• A002750 (program): Sum of logarithmic numbers.
• A002751 (program): Sum of logarithmic numbers.
• A002752 (program): a(n) = Fibonacci(n-1) mod n.
• A002754 (program): Related to coefficient of m in Jacobi elliptic function cn(z, m).
• A002760 (program): Squares and cubes.
• A002775 (program): a(n) = n^2 * n!.
• A002776 (program): Terms in certain determinants.
• A002783 (program): 2*(3^n - 2^n) + 1.
• A002789 (program): Number of integer points in a certain quadrilateral scaled by a factor of n.
• A002791 (program): a(n) = Sum_{d|n, d <= 4} d^2 + 4*Sum_{d|n, d>4} d.
• A002793 (program): a(n) = 2n*a(n-1) - (n-1)^2*a(n-2).
• A002797 (program): Number of solutions to a linear inequality.
• A002798 (program): a(n) = a(n-2)+a(n-3)-a(n-5).
• A002799 (program): Number of 4-line partitions of n (i.e., planar partitions of n with at most 4 lines).
• A002801 (program): a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) with a(0) = a(1) = 1.
• A002802 (program): a(n) = (2*n+3)!/(6*n!*(n+1)!).
• A002803 (program): a(n) = (2n+4)!/(4!*n!*(n+1)!).
• A002804 (program): (Presumed) solution to Waring’s problem: g(n) = 2^n + floor((3/2)^n) - 2.
• A002805 (program): Denominators of harmonic numbers H(n) = Sum_{i=1..n} 1/i.
• A002807 (program): a(n) = Sum_{k=3..n} (k-1)!*C(n,k)/2.
• A002808 (program): The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
• A002815 (program): a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.
• A002817 (program): Doubly triangular numbers: a(n) = n*(n+1)*(n^2+n+2)/8.
• A002818 (program): Nearest integer to exp n^2.
• A002819 (program): Liouville’s function L(n) = partial sums of A008836.
• A002820 (program): Number of n X n invertible binary matrices A such that A+I is invertible.
• A002821 (program): a(n) = nearest integer to n^(3/2).
• A002822 (program): Numbers m such that 6m-1, 6m+1 are twin primes.
• A002825 (program): Number of precomplete Post functions.
• A002865 (program): Number of partitions of n that do not contain 1 as a part.
• A002866 (program): a(0) = 1; for n > 0, a(n) = 2^(n-1)*n!.
• A002867 (program): a(n) = binomial(n,floor(n/2))*(n+1)!.
• A002868 (program): Largest number in n-th row of triangle of Lah numbers (A008297 and A271703).
• A002869 (program): Largest number in n-th row of triangle A019538.
• A002870 (program): Largest Stirling numbers of second kind: a(n) = max_{k=1..n} S2(n,k).
• A002871 (program): a(n) = max_{k=0..n} 2^k*A048993(n,k)
• A002878 (program): Bisection of Lucas sequence: a(n) = L(2*n+1).
• A002884 (program): Number of nonsingular n X n matrices over GF(2) (order of the group GL(n,2)); order of Chevalley group A_n (2); order of projective special linear group PSL_n(2).
• A002893 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k).
• A002894 (program): a(n) = binomial(2n, n)^2.
• A002896 (program): Number of 2n-step polygons on cubic lattice.
• A002897 (program): a(n) = binomial(2n,n)^3.
• A002898 (program): Number of n-step closed paths on hexagonal lattice.
• A002901 (program): n^3 - floor( n/3 ).
• A002908 (program): High temperature expansion of -u/J in odd powers of v = tanh(J/kT), where u is energy per site of the spin-1/2 Ising model on square lattice with nearest-neighbor interaction J at temperature T.
• A002928 (program): Magnetization for square lattice.
• A002938 (program): The minimal sequence (from solving n^3 - m^2 = a(n)).
• A002939 (program): a(n) = 2*n*(2*n-1).
• A002940 (program): Arrays of dumbbells.
• A002941 (program): Arrays of dumbbells.
• A002942 (program): a(n) = n^2 written backwards.
• A002943 (program): a(n) = 2*n*(2*n+1).
• A002944 (program): a(n) = LCM(1,2,…,n) / n.
• A002960 (program): The square sieve.
• A002965 (program): Interleave denominators (A000129) and numerators (A001333) of convergents to sqrt(2).
• A002970 (program): Numbers n such that 4*n^2 + 9 is prime.
• A002971 (program): Numbers k such that 4*k^2 + 25 is prime.
• A002984 (program): a(0) = 1; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
• A002993 (program): Initial digits of squares.
• A002994 (program): Initial digit of cubes.
• A002999 (program): Expansion of (1+x*exp(x))^2.
• A003000 (program): Number of bifix-free (or primary, or unbordered) words of length n over a two-letter alphabet.
• A003011 (program): Number of permutations of up to n kinds of objects, where each kind of object can occur at most two times.
• A003013 (program): E.g.f. 1+x*exp(x)+x^2*exp(2*x).
• A003014 (program): Expansion of e.g.f.: 1 + x*exp(x) + x^2*exp(2*x) + x^3*exp(3*x).
• A003031 (program): Denominators of expansion of Fresnel integral S(z).
• A003034 (program): Sylvester’s problem: minimal number of ordinary lines through n points in the plane.
• A003035 (program): Maximal number of 3-tree rows in n-tree orchard problem.
• A003036 (program): Number of simplicial arrangements of n lines in the plane (the lines do not pass through a common point, all cells are triangles).
• A003046 (program): Product of first n Catalan numbers.
• A003047 (program): a(n) = Catalan(n) * Product a(k), k = 0 . . n-1.
• A003048 (program): a(n+1) = n*a(n) - (-1)^n.
• A003052 (program): Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).
• A003053 (program): Order of orthogonal group O(n, GF(2)).
• A003056 (program): n appears n+1 times. Also the array A(n,k) = n+k (n >= 0, k >= 0) read by antidiagonals. Also inverse of triangular numbers.
• A003057 (program): n appears n - 1 times.
• A003059 (program): k appears 2k-1 times. Also, square root of n, rounded up.
• A003063 (program): a(n) = 3^(n-1) - 2^n.
• A003070 (program): a(n) = ceiling(log_2 n!).
• A003071 (program): Sorting numbers: maximal number of comparisons for sorting n elements by list merging.
• A003074 (program): Number of different numbers <= n that are sums of 3 positive cubes.
• A003075 (program): Minimal number of comparisons needed for n-element sorting network.
• A003076 (program): n-th digit after decimal point of square root of n.
• A003079 (program): One of the basic cycles in the x->3x-1 (x odd) or x/2 (x even) problem.
• A003082 (program): Number of multigraphs with 4 nodes and n edges.
• A003091 (program): a(n) = floor( 2^(n*(n-1)/2) / n! ).
• A003095 (program): a(n) = a(n-1)^2 + 1 for n >= 1, with a(0) = 0.
• A003099 (program): a(n) = Sum_{k=0..n} binomial(n,k^2).
• A003101 (program): a(n) = Sum_{k = 1..n} (n - k + 1)^k.
• A003105 (program): Schur’s 1926 partition theorem: number of partitions of n into parts 6n+1 or 6n-1.
• A003106 (program): Number of partitions of n into parts 5k+2 or 5k+3.
• A003107 (program): Number of partitions of n into Fibonacci parts (with a single type of 1).
• A003108 (program): Number of partitions of n into cubes.
• A003114 (program): Number of partitions of n into parts 5k+1 or 5k+4.
• A003115 (program): a(n) = 4^floor(n/2)*a(n-1) - a(n-2), for n >= 2, with a(0) = a(1) = 1.
• A003124 (program): One of the basic cycles in the x->3x-1 (x odd) or x/2 (x even) problem.
• A003128 (program): Number of driving-point impedances of an n-terminal network.
• A003132 (program): Sum of squares of digits of n.
• A003136 (program): Loeschian numbers: numbers of the form x^2 + xy + y^2; norms of vectors in A2 lattice.
• A003138 (program): Nearest integer to 24*(2^n - 1)/n.
• A003141 (program): Minimal number of arcs whose reversal yields a transitive tournament.
• A003143 (program): a(2*n) = floor( 17*2^n/14 ), a(2*n+1) = floor( 12*2^n/7 ).
• A003144 (program): Positions of letter a in the tribonacci word abacabaabacababac… generated by a->ab, b->ac, c->a (cf. A092782).
• A003145 (program): Positions of letter b in the tribonacci word abacabaabacababac… generated by a->ab, b->ac, c->a (cf. A092782).
• A003146 (program): Positions of letter c in the tribonacci word abacabaabacababac… generated by a->ab, b->ac, c->a (cf. A092782).
• A003148 (program): a(n+1) = a(n) + 2n*(2n+1)*a(n-1), with a(0) = a(1) = 1.
• A003149 (program): a(n) = Sum_{k=0..n} k!(n-k)!.
• A003151 (program): Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))).
• A003152 (program): A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2))).
• A003153 (program): a(n) = integer nearest n*(1+sqrt(2)).
• A003154 (program): Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1.
• A003156 (program): A self-generating sequence (see Comments for definition).
• A003157 (program): A self-generating sequence (see Comments in A003156 for the definition).
• A003158 (program): A self-generating sequence (see Comments in A003156 for the definition).
• A003159 (program): Numbers n whose binary representation ends in an even number of zeros.
• A003160 (program): a(1) = a(2) = 1, a(n) = n - a(a(n-1)) - a(a(n-2)).
• A003161 (program): A binomial coefficient sum.
• A003165 (program): a(n) = floor(n/2) + 1 - d(n), where d(n) is the number of divisors of n.
• A003168 (program): Number of blobs with 2n+1 edges.
• A003169 (program): Number of 2-line arrays; or number of P-graphs with 2n edges.
• A003176 (program): Integer part of 24(2^n-1)/n.
• A003177 (program): a(n) = ceiling(24(2^n-1)/n).
• A003185 (program): a(n) = (4*n+1)(4*n+5).
• A003188 (program): Decimal equivalent of Gray code for n.
• A003215 (program): Hex (or centered hexagonal) numbers: 3*n*(n+1)+1 (crystal ball sequence for hexagonal lattice).
• A003221 (program): Number of even permutations of length n with no fixed points.
• A003222 (program): a(n) = 2^(3*n+1) - 2*n*(2*n+1).
• A003229 (program): a(n) = a(n-1) + 2*a(n-3) with a(0)=a(1)=1, a(2)=3.
• A003230 (program): Expansion of 1/((1-x)*(1-2*x)*(1-x-2*x^3)).
• A003231 (program): a(n) = floor(n*(sqrt(5)+5)/2).
• A003232 (program): Expansion of (x-1)*(x^2-4*x-1)/(1-2*x)^2.
• A003233 (program): Numbers k such that A003231(A001950(k)) = A001950(A003231(k)).
• A003234 (program): Numbers k such that A003231(A001950(k)) = A001950(A003231(k)) - 1.
• A003235 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C(k^2,n).
• A003236 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C((k+1)^2, n).
• A003238 (program): Number of rooted trees with n vertices in which vertices at the same level have the same degree.
• A003239 (program): Number of rooted planar trees with n non-root nodes: circularly cycling the subtrees at the root gives equivalent trees.
• A003242 (program): Number of compositions of n such that no two adjacent parts are equal (Carlitz compositions).
• A003249 (program): a(n) = A001950(A003234(n)) + 1.
• A003250 (program): The number m such that A001950(m) = A003231(A003234(n)).
• A003251 (program): Complement of A003250.
• A003252 (program): The number m such that A003251(m) = A003231(n).
• A003253 (program): Complement of A003252.
• A003256 (program): a(n) is the number m such that A242094(m) = A001950(n).
• A003257 (program): Complement of A003256.
• A003258 (program): The number m such that c’(m) = A005206(A003231(n)), where c’(m) = A249115(m) is the m-th positive integer not in A003231.
• A003259 (program): Complement of A003258.
• A003261 (program): Woodall (or Riesel) numbers: n*2^n - 1.
• A003265 (program): Not representable by truncated tribonacci sequence 2, 4, 7, 13, 24, 44, 81, ….
• A003266 (program): Product of first n nonzero Fibonacci numbers F(1), …, F(n).
• A003269 (program): a(n) = a(n-1) + a(n-4) with a(0) = 0, a(1) = a(2) = a(3) = 1.
• A003270 (program): A nonrepetitive sequence.
• A003274 (program): Number of key permutations of length n: permutations {a_i} with |a_i-a_{i-1}| = 1 or 2.
• A003277 (program): Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(n) = 1.
• A003278 (program): Szekeres’s sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), …, a(n-1), k.
• A003292 (program): Number of 4-line partitions of n decreasing across rows.
• A003308 (program): a(n) = 2*n^(n-2).
• A003312 (program): a(1) = 3; for n>0, a(n+1) = a(n) + floor((a(n)-1)/2).
• A003314 (program): Binary entropy function: a(1)=0; for n > 1, a(n) = n + min { a(k)+a(n-k) : 1 <= k <= n-1 }.
• A003318 (program): a(n + 1) = 1 + a( floor(n/1) ) + a( floor(n/2) ) + … + a( floor(n/n) ).
• A003319 (program): Number of connected permutations of [1..n] (those not fixing [1..j] for 0 < j < n). Also called indecomposable permutations, or irreducible permutations.
• A003320 (program): a(n) = max_{k=0..n} k^(n-k).
• A003324 (program): A nonrepetitive sequence.
• A003325 (program): Numbers that are the sum of 2 positive cubes.
• A003402 (program): G.f.: 1/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^5)).
• A003408 (program): a(n) = binomial(3n+6, n).
• A003409 (program): a(n) = 3*binomial(2n-1,n).
• A003410 (program): Expansion of (1+x)(1+x^2)/(1-x-x^3).
• A003411 (program): Losing initial positions in game: two players alternate in removing >= 1 stones; last player wins; first player may not remove all stones; each move <= 3 times previous move.
• A003413 (program): From a nim-like game.
• A003415 (program): a(n) = n’ = arithmetic derivative of n: a(0) = a(1) = 0, a(prime) = 1, a(mn) = m*a(n) + n*a(m).
• A003417 (program): Continued fraction for e.
• A003418 (program): Least common multiple (or LCM) of {1, 2, …, n} for n >= 1, a(0) = 1.
• A003422 (program): Left factorials: !n = Sum_{k=0..n-1} k!.
• A003434 (program): Number of iterations of phi(x) at n needed to reach 1.
• A003435 (program): Number of directed Hamiltonian circuits on n-octahedron with a marked starting node.
• A003436 (program): Number of inequivalent labeled Hamiltonian circuits on n-octahedron. Interlacing chords joining 2n points on circle.
• A003440 (program): Number of binary vectors with restricted repetitions.
• A003441 (program): Number of nonequivalent dissections of a polygon into n triangles by nonintersecting diagonals rooted at a cell up to rotation.
• A003451 (program): Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation.
• A003452 (program): Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
• A003453 (program): Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation and reflection.
• A003461 (program): Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).
• A003462 (program): a(n) = (3^n - 1)/2.
• A003463 (program): a(n) = (5^n - 1)/4.
• A003464 (program): a(n) = (6^n - 1)/5.
• A003467 (program): Number of minimal covers of an n-set that cover exactly 3 points uniquely.
• A003468 (program): Number of minimal 3-covers of a labeled n-set.
• A003469 (program): Number of minimal covers of an (n + 1)-set by a collection of n nonempty subsets, a(n) = A035348(n,n-1).
• A003470 (program): a(n) = n*a(n-1) - a(n-2) + 1 + (-1)^n.
• A003472 (program): a(n) = 2^(n-4)*C(n,4).
• A003476 (program): a(n) = a(n-1) + 2a(n-3).
• A003477 (program): Expansion of 1/((1-2x)(1+x^2)(1-x-2x^3)).
• A003478 (program): Expansion of 1/(1-2x)(1-x-2x^3).
• A003479 (program): Expansion of 1/((1-x)*(1-x-2*x^3)).
• A003480 (program): a(n) = 4*a(n-1) - 2*a(n-2) (n >= 3).
• A003481 (program): a(n) = 7*a(n-1) - a(n-2) + 5.
• A003482 (program): a(n) = 7*a(n-1) - a(n-2) + 4, with a(0) = 0, a(1) = 5.
• A003484 (program): Radon function, also called Hurwitz-Radon numbers.
• A003485 (program): Hurwitz-Radon function at powers of 2.
• A003486 (program): a(n) = (n^2 + 1)*3^n.
• A003499 (program): a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.
• A003500 (program): a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4.
• A003501 (program): a(n) = 5*a(n-1) - a(n-2), with a(0) = 2, a(1) = 5.
• A003504 (program): a(0)=a(1)=1; thereafter a(n+1) = (1/n)*Sum_{k=0..n} a(k)^2 (a(n) is not always integral!).
• A003506 (program): Triangle of denominators in Leibniz’s Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
• A003508 (program): a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
• A003511 (program): A Beatty sequence: floor( n * (1 + sqrt(3))/2 ).
• A003512 (program): A Beatty sequence: floor(n*(sqrt(3) + 2)).
• A003516 (program): Binomial coefficients C(2n+1, n-2).
• A003517 (program): Number of permutations of [n+1] with exactly 1 increasing subsequence of length 3.
• A003518 (program): a(n) = 8*binomial(2*n+1,n-3)/(n+5).
• A003519 (program): a(n) = 10*C(2n+1, n-4)/(n+6).
• A003520 (program): a(n) = a(n-1) + a(n-5); a(0) = … = a(4) = 1.
• A003522 (program): a(n) = Sum_{k=0..n} C(n-k,3k).
• A003524 (program): Divisors of 2^12 - 1.
• A003527 (program): Divisors of 2^16 - 1.
• A003539 (program): a(n)=3*a(n-1)+16 (the first 11 terms are primes).
• A003555 (program): Sum{1,2,…,(10^n - 1)/9}, or (10^n -1)/9)((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).
• A003557 (program): n divided by largest squarefree divisor of n; if n = Product p(k)^e(k) then a(n) = Product p(k)^(e(k)-1), with a(1) = 1.
• A003558 (program): Least number m > 0 such that 2^m == +-1 (mod 2n + 1).
• A003559 (program): Least number m such that 3^m = +- 1 mod 3n + 1.
• A003560 (program): Least number m such that 4^m = +- 1 mod 4n + 1.
• A003561 (program): Least number m such that 5^m = +- 1 mod 5n + 1.
• A003562 (program): Least number m such that 6^m = +- 1 mod 6n + 1.
• A003564 (program): Least number m such that 8^m = +- 1 mod 8n + 1.
• A003565 (program): Least number m such that 9^m = +- 1 mod 9n + 1.
• A003566 (program): Least number m such that 10^m = +- 1 mod 10n + 1.
• A003568 (program): Least number m such that 12^m = +- 1 mod 12n + 1.
• A003569 (program): a(n) = least positive number m such that 4^m == +1 or -1 mod 2n + 1, with a(0) = 0 by convention.
• A003570 (program): a(n) = least positive number m such that 8^m == +1 or -1 mod 2n + 1, with a(0) = 0 by convention.
• A003571 (program): Order of 3 mod 3n+1.
• A003572 (program): Order of 3 mod 3n+2.
• A003573 (program): Order of 4 mod 4n+1.
• A003574 (program): Order of 4 mod 4n-1.
• A003575 (program): Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=3.
• A003576 (program): Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=4.
• A003577 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=5.
• A003578 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x) - 1)/b), with b=6.
• A003579 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x) - 1)/b), with b=7.
• A003580 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=8.
• A003581 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=9.
• A003582 (program): Dowling numbers: e.g.f. exp(x + (exp(b*x)-1)/b) with b=10.
• A003583 (program): a(n) = (n+2)*2^(2*n-1) - (n/2)*binomial(2*n,n).
• A003584 (program): Unicursal (i.e., possessing an Eulerian path) planar rooted maps with n edges.
• A003586 (program): 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.
• A003589 (program): a(n) has the property that the sequence b(n) = number of 2’s between successive 3’s is the same as the original sequence.
• A003592 (program): Numbers of the form 2^i*5^j with i, j >= 0.
• A003600 (program): Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6 (n > 0).
• A003601 (program): Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n). Alternatively, tau(n) (A000005(n)) divides sigma(n) (A000203(n)).
• A003602 (program): Kimberling’s paraphrases: if n = (2k-1)*2^m then a(n) = k.
• A003603 (program): Fractal sequence obtained from Fibonacci numbers (or Wythoff array).
• A003605 (program): Unique monotonic sequence of nonnegative integers satisfying a(a(n)) = 3n.
• A003608 (program): Add 4, then reverse digits; start with 0.
• A003619 (program): Not of form [ e^m ], m >= 1.
• A003622 (program): The Wythoff compound sequence AA: a(n) = floor(n*phi^2) - 1, where phi = (1+sqrt(5))/2.
• A003623 (program): Wythoff AB-numbers: floor(floor(n*phi^2)*phi), where phi = (1+sqrt(5))/2.
• A003625 (program): Primes congruent to {3, 5, 6} mod 7.
• A003626 (program): Inert rational primes in Q(sqrt(-5)).
• A003627 (program): Primes of the form 3n-1.
• A003628 (program): Primes congruent to {5, 7} mod 8.
• A003629 (program): Primes p == +- 3 (mod 8), or, primes p such that 2 is not a square mod p.
• A003630 (program): Inert rational primes in Q[sqrt(3)].
• A003631 (program): Primes congruent to 2 or 3 modulo 5.
• A003640 (program): Number of genera of imaginary quadratic field with discriminant -k, k = A003657(n).
• A003641 (program): Number of genera of imaginary quadratic field with discriminant -k, k = A039957(n).
• A003642 (program): Number of genera of imaginary quadratic field with discriminant -k, k = A191483(n).
• A003645 (program): a(n) = 2^n * C(n+1), where C(n) = A000108(n) Catalan numbers.
• A003657 (program): Discriminants of imaginary quadratic fields, negated.
• A003658 (program): Fundamental discriminants of real quadratic fields; indices of primitive positive Dirichlet L-series.
• A003662 (program): a(n) is smallest number != a(j)+a(k), j<k.
• A003663 (program): a(n) is smallest number != a(j)+a(k), j<k.
• A003664 (program): a(n) is smallest number larger than a(n-1) and not = a(j)+a(k), j<k.
• A003665 (program): a(n) = 2^(n-1)*( 2^n + (-1)^n ).
• A003673 (program): Decimal expansion of fine-structure constant alpha.
• A003674 (program): 2^(n-1)*( 2^n - (-1)^n ).
• A003677 (program): Decimal expansion of proton mass (mass units).
• A003682 (program): Number of (undirected) Hamiltonian paths in the n-ladder graph K_2 X P_n.
• A003683 (program): a(n) = 2^(n-1)*(2^n - (-1)^n)/3.
• A003686 (program): Number of genealogical 1-2 rooted trees of height n.
• A003687 (program): a(n+1) = a(n)-a(1)a(2)…a(n-1), if n>0. a(0)=1, a(1)=2.
• A003688 (program): a(n) = 3*a(n-1) + a(n-2), with a(1)=1 and a(2)=4.
• A003689 (program): Number of Hamiltonian paths in K_3 X P_n.
• A003690 (program): Number of spanning trees in K_3 X P_n.
• A003691 (program): Number of spanning trees with degrees 1 and 3 in K_3 X P_2n.
• A003692 (program): Number of trees on n labeled vertices with degree at most 3.
• A003693 (program): Number of 2-factors in P_4 X P_n.
• A003698 (program): Number of 2-factors in C_4 X P_n.
• A003699 (program): Number of Hamiltonian cycles in C_4 X P_n.
• A003701 (program): Expansion of e.g.f. exp(x)/cos(x).
• A003703 (program): Expansion of e.g.f. cos(log(1+x)).
• A003709 (program): E.g.f. cos(sin(x)) (even powers only).
• A003712 (program): E.g.f. sin(sin(x)) (odd powers only).
• A003713 (program): Expansion of e.g.f. log(1/(1+log(1-x))).
• A003714 (program): Fibbinary numbers: if n = F(i1) + F(i2) + … + F(ik) is the Zeckendorf representation of n (i.e., write n in Fibonacci number system) then a(n) = 2^(i1 - 2) + 2^(i2 - 2) + … + 2^(ik - 2). Also numbers whose binary representation contains no two adjacent 1’s.
• A003719 (program): Expansion of tan(x)*cosh(x).
• A003724 (program): Number of partitions of n-set into odd blocks.
• A003725 (program): E.g.f.: exp( x * exp(-x) ).
• A003726 (program): Numbers with no 3 adjacent 1’s in binary expansion.
• A003727 (program): Expansion of e.g.f. exp(x * cosh(x)).
• A003731 (program): Number of Hamiltonian cycles in C_5 X P_n.
• A003739 (program): Number of spanning trees in W_5 X P_n.
• A003747 (program): Number of perfect matchings (or domino tilings) in K_5 X P_2n.
• A003751 (program): Number of spanning trees in K_5 x P_n.
• A003753 (program): Number of spanning trees in C_4 X P_n.
• A003754 (program): Numbers with no adjacent 0’s in binary expansion.
• A003755 (program): Number of spanning trees in S_4 X P_n.
• A003757 (program): Number of perfect matchings (or domino tilings) in D_4 X P_(n-1).
• A003758 (program): Number of 2-factors in D_4 X P_n.
• A003759 (program): Number of Hamiltonian cycles in D_4 X P_n.
• A003767 (program): Number of spanning trees in (K_4 - e) X P_n.
• A003769 (program): Number of perfect matchings (or domino tilings) in K_4 X P_n.
• A003770 (program): Number of 2-factors in K_4 X P_n.
• A003771 (program): Number of Hamiltonian cycles in K_4 X P_n.
• A003773 (program): Number of spanning trees in K_4 X P_n.
• A003775 (program): Number of perfect matchings (or domino tilings) in P_5 X P_2n.
• A003777 (program): a(n) = n^3 + n^2 - 1.
• A003787 (program): Order of universal Chevalley group A_n (3).
• A003796 (program): Numbers with no 3 adjacent 0’s in binary expansion.
• A003800 (program): Order of universal Chevalley group A_2 (q), q = prime power.
• A003815 (program): a(0) = 0, a(n) = a(n-1) XOR n.
• A003816 (program): a(0) = 0, a(n) = a(n-1) XOR -n.
• A003817 (program): a(0) = 0, a(n) = a(n-1) OR n.
• A003823 (program): Power series expansion of the Rogers-Ramanujan continued fraction 1+x/(1+x^2/(1+x^3/(1+x^4/(1+…)))).
• A003841 (program): Order of universal Chevalley group D_2(q), q = prime power.
• A003842 (program): The infinite Fibonacci word: start with 1, repeatedly apply the morphism 1->12, 2->1, take limit; or, start with S(0)=2, S(1)=1, and for n>1 define S(n)=S(n-1)S(n-2), then the sequence is S(oo).
• A003848 (program): Order of (usually) simple Chevalley group D_2(q), q = prime power.
• A003849 (program): The infinite Fibonacci word (start with 0, apply 0->01, 1->0, take limit).
• A003870 (program): Degrees of irreducible representations of symmetric group S_6.
• A003878 (program): n^4+(9/2)*n^3+n^2-(9/2)*n+1.
• A003881 (program): Decimal expansion of Pi/4.
• A003884 (program): Degrees of irreducible representations of group L2(16).
• A003885 (program): Degrees of irreducible representations of group L2(17).
• A003886 (program): Degrees of irreducible representations of group L2(19).
• A003887 (program): Degrees of irreducible representations of group L2(23).
• A003888 (program): Degrees of irreducible representations of group L2(25).
• A003889 (program): Degrees of irreducible representations of group L2(27).
• A003890 (program): Degrees of irreducible representations of group L2(29).
• A003891 (program): Degrees of irreducible representations of group L2(31).
• A003892 (program): Degrees of irreducible representations of group L2(32).
• A003893 (program): a(n) = Fibonacci(n) mod 10.
• A003931 (program): Order of universal Chevalley group B_2(q), q = prime power.
• A003938 (program): Order of (usually) simple Chevalley group B_2(q), q = prime power.
• A003945 (program): Expansion of g.f. (1+x)/(1-2*x).
• A003946 (program): Expansion of (1+x)/(1-3*x).
• A003947 (program): Expansion of (1+x)/(1-4*x).
• A003948 (program): Expansion of (1+x)/(1-5*x).
• A003949 (program): Expansion of g.f.: (1+x)/(1-6*x).
• A003950 (program): Expansion of g.f.: (1+x)/(1-7*x).
• A003951 (program): Expansion of g.f.: (1+x)/(1-8*x).
• A003952 (program): Expansion of g.f.: (1+x)/(1-9*x).
• A003953 (program): Expansion of g.f.: (1+x)/(1-10*x).
• A003954 (program): Expansion of g.f.: (1+x)/(1-11*x).
• A003955 (program): a(n) = (2*n + 4) * (1*3*5*…*(2*n+1))^2.
• A003958 (program): If n = Product p(k)^e(k) then a(n) = Product (p(k)-1)^e(k).
• A003959 (program): If n = Product p(k)^e(k) then a(n) = Product (p(k)+1)^e(k), a(1) = 1.
• A003960 (program): Fully multiplicative with a(p) = [ (p+1)/2 ] for prime p.
• A003961 (program): Completely multiplicative with a(prime(k)) = prime(k+1).
• A003962 (program): Completely multiplicative with a(p(k)) = floor( (p(k+1)+1)/2 ) for k-th prime p(k).
• A003963 (program): Fully multiplicative with a(p) = k if p is the k-th prime.
• A003965 (program): Fully multiplicative with a(prime(k)) = Fibonacci(k+2).
• A003966 (program): Möbius transform of A003958.
• A003967 (program): Inverse Möbius transform of A003958.
• A003968 (program): Möbius transform of A003959.
• A003969 (program): Inverse Möbius transform of A003959.
• A003971 (program): Inverse Möbius transform of A003960.
• A003972 (program): Moebius transform of A003961; a(n) = phi(A003961(n)), where A003961 shifts the prime factorization of n one step towards the larger primes.
• A003973 (program): Inverse Möbius transform of A003961; a(n) = sigma(A003961(n)), where A003961 shifts the prime factorization of n one step towards the larger primes.
• A003975 (program): Inverse Möbius transform of A003962.
• A003977 (program): Inverse Möbius transform of A003963.
• A003981 (program): Inverse Möbius transform of A003965.
• A003982 (program): Table read by rows: 1 if x = y, 0 otherwise, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),…
• A003983 (program): Array read by antidiagonals with T(n,k) = min(n,k).
• A003984 (program): Table of max(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),…
• A003985 (program): Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is i AND j.
• A003986 (program): Table of x OR y, where (x,y) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), …
• A003987 (program): Table of n XOR m (or Nim-sum of n and m) read by antidiagonals, i.e., with entries in the order (n,m) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), …
• A003988 (program): Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is [ i/j ].
• A003989 (program): Triangle T from the array A(x, y) = gcd(x,y), for x >= 1, y >= 1, read by antidiagonals.
• A003990 (program): Table of lcm(x,y), read along antidiagonals.
• A003991 (program): Multiplication table read by antidiagonals: T(i,j) = i*j, i>=1, j>=1.
• A003992 (program): Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.
• A003993 (program): Sequence b_3 (n) arising from homology of partitions with even number of blocks.
• A004000 (program): RATS: Reverse Add Then Sort the digits applied to previous term, starting with 1.
• A004001 (program): Hofstadter-Conway $10000 sequence: a(n) = a(a(n-1)) + a(n-a(n-1)) with a(1) = a(2) = 1.
• A004004 (program): a(n) = (3^{2n+1} - 8*n - 3)/16.
• A004006 (program): a(n) = C(n,1) + C(n,2) + C(n,3), or n*(n^2 + 5)/6.
• A004009 (program): Expansion of Eisenstein series E_4(q) (alternate convention E_2(q)); theta series of E_8 lattice.
• A004011 (program): Theta series of D_4 lattice; Fourier coefficients of Eisenstein series E_{gamma,2}.
• A004013 (program): Theta series of body-centered cubic (b.c.c.) lattice.
• A004015 (program): Theta series of face-centered cubic (f.c.c.) lattice.
• A004016 (program): Theta series of planar hexagonal lattice A_2.
• A004017 (program): Theta series of E_8 lattice with respect to deep hole.
• A004018 (program): Theta series of square lattice (or number of ways of writing n as a sum of 2 squares). Often denoted by r(n) or r_2(n).
• A004019 (program): a(0) = 0; for n > 0, a(n) = (a(n-1) + 1)^2.
• A004020 (program): Theta series of square lattice with respect to edge.
• A004024 (program): Theta series of b.c.c. lattice with respect to deep hole.
• A004025 (program): Theta series of b.c.c. lattice with respect to long edge.
• A004040 (program): Inversion of A000257.
• A004041 (program): Scaled sums of odd reciprocals: a(n) = (2*n + 1)!!*(Sum_{k=0..n} 1/(2*k + 1)).
• A004043 (program): The coding-theoretic function A(n,8,8).
• A004047 (program): The coding-theoretic function A(n,10,9).
• A004050 (program): Numbers of the form 2^j + 3^k, for j and k >= 0.
• A004052 (program): The coding-theoretic function A(n,14,8).
• A004054 (program): Expansion of (1-x)/((1+x)*(1-2*x)*(1-3*x)).
• A004055 (program): ((p-1)/2)! mod p for odd primes p.
• A004056 (program): The coding-theoretic function A(n,14,12).
• A004057 (program): Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)).
• A004058 (program): Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)).
• A004068 (program): Number of atoms in a decahedron with n shells.
• A004070 (program): Table of Whitney numbers W(n,k) read by antidiagonals, where W(n,k) is maximal number of pieces into which n-space is sliced by k hyperplanes, n >= 0, k >= 0.
• A004074 (program): a(n) = 2*A004001(n) - n, where A004001 is the Hofstadter-Conway $10000 sequence.
• A004079 (program): a(n) = maximal m such that an m X n Florentine rectangle exists.
• A004082 (program): Numbers k such that sin(k-1) <= 0 and sin(k) > 0.
• A004083 (program): Numbers k such that cos(k-1) <= 0 and cos(k) > 0.
• A004084 (program): a(n) = n-th positive integer k such that tan(k-1) <= 0 and tan(k) > 0.
• A004085 (program): Sum of digits of Euler totient function of n.
• A004086 (program): Read n backwards (referred to as R(n) in many sequences).
• A004087 (program): Primes written backwards.
• A004088 (program): Sum of digits of number of partitions of n.
• A004089 (program): Reverse digits of number of partitions of n.
• A004090 (program): Sum of digits of Fibonacci numbers.
• A004091 (program): Fibonacci numbers written backwards.
• A004092 (program): Sum of digits of even numbers.
• A004093 (program): Even numbers written backwards.
• A004094 (program): Powers of 2 written backwards.
• A004095 (program): Sum of digits of Catalan numbers.
• A004096 (program): Catalan numbers written backwards.
• A004097 (program): Sum of digits of Bell numbers.
• A004098 (program): Bell numbers written backwards.
• A004099 (program): Sum of digits of Euler numbers.
• A004116 (program): a(n) = floor((n^2 + 6n - 3)/4).
• A004117 (program): Numerators of expansion of (1-x)^(-1/3).
• A004119 (program): a(0)=1; thereafter a(n) = 3*2^(n-1)+1.
• A004120 (program): Expansion of (1 + x - x^5) / (1 - x)^3.
• A004123 (program): Number of generalized weak orders on n points.
• A004125 (program): Sum of remainders of n mod k, for k = 1, 2, 3, …, n.
• A004126 (program): a(n) = n*(7*n^2 - 1)/6.
• A004128 (program): a(n) = Sum_{k=1..n} floor(3*n/3^k).
• A004130 (program): Numerators in expansion of (1-x)^{-1/4}.
• A004131 (program): Modular postage stamp problem: largest m such that there exists an n-subset S of nonnegative integers such that 0,…,m-1 can be expressed as a mod-m sum of two distinct elements of S.
• A004134 (program): Denominators in expansion of (1-x)^{-1/4} are 2^a(n).
• A004138 (program): From a counter moving problem.
• A004139 (program): Odd primes excluding 5.
• A004140 (program): Number of nonempty labeled simple graphs on nodes chosen from an n-set.
• A004141 (program): Norm of a matrix.
• A004142 (program): n*(3^n-2^n).
• A004144 (program): Nonhypotenuse numbers (indices of positive squares that are not the sums of 2 distinct nonzero squares).
• A004146 (program): Alternate Lucas numbers - 2.
• A004148 (program): Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).
• A004150 (program): Euler numbers written backwards.
• A004151 (program): Omit trailing zeros from n.
• A004152 (program): Sum of digits of n!.
• A004153 (program): Factorial numbers written backwards.
• A004154 (program): Omit trailing zeros from factorial numbers.
• A004155 (program): Sum of digits of n-th odd number.
• A004156 (program): Odd numbers written backwards.
• A004157 (program): Sum of digits of n-th triangular number.
• A004158 (program): Triangular numbers written backwards.
• A004159 (program): Sum of digits of n^2.
• A004160 (program): Sum of digits of tetrahedral numbers.
• A004161 (program): Tetrahedral numbers written backwards.
• A004162 (program): Sum of digits of pentagonal numbers.
• A004163 (program): Pentagonal numbers written backwards.
• A004164 (program): Sum of digits of n^3.
• A004165 (program): Cubes written backwards.
• A004166 (program): Sum of digits of 3^n.
• A004167 (program): Powers of 3 written backwards.
• A004169 (program): Values of m for which a regular polygon with m sides cannot be constructed with ruler and compass.
• A004171 (program): a(n) = 2^(2n+1).
• A004174 (program): Triangle of coefficients of Euler polynomials 2^n*E_n(x) (exponents in increasing order).
• A004175 (program): Triangle of coefficients of Euler polynomials 2^n*E_n(x) (exponents in decreasing order).
• A004183 (program): Omit 8’s from n.
• A004184 (program): Omit 9’s from n.
• A004185 (program): Arrange digits of n in increasing order, then (for n > 0) omit the zeros.
• A004186 (program): Arrange digits of n in decreasing order.
• A004187 (program): a(n) = 7*a(n-1) - a(n-2) with a(0) = 0, a(1) = 1.
• A004188 (program): a(n) = n*(3*n^2 - 1)/2.
• A004189 (program): a(n) = 10*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
• A004190 (program): Expansion of 1/(1 - 11*x + x^2).
• A004191 (program): Expansion of 1/(1 - 12*x + x^2).
• A004197 (program): Table of min(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),…
• A004198 (program): Table of x AND y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),…
• A004199 (program): Table of [ x/y ], where (x,y) = (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),…
• A004200 (program): Continued fraction for Sum_{k>=0} 1/3^(2^k).
• A004201 (program): Accept one, reject one, accept two, reject two, …
• A004202 (program): Skip 1, take 1, skip 2, take 2, skip 3, take 3, etc.
• A004207 (program): a(0) = 1, a(n) = sum of digits of all previous terms.
• A004208 (program): a(n) = n * (2*n - 1)!! - Sum_{k=0..n-1} a(k) * (2*n - 2*k - 1)!!.
• A004211 (program): Shifts one place left under 2nd-order binomial transform.
• A004212 (program): Shifts one place left under 3rd-order binomial transform.
• A004213 (program): Shifts one place left under 4th-order binomial transform.
• A004214 (program): Positive numbers that are not the sum of three nonzero squares.
• A004215 (program): Numbers that are the sum of 4 but no fewer nonzero squares.
• A004216 (program): a(n) = floor(log_10(n)).
• A004218 (program): log_10(n) rounded up.
• A004219 (program): a(n) = floor(10*log_10(n)).
• A004220 (program): 10*log_10 (n) rounded to nearest integer.
• A004221 (program): 10*log_10 (n) rounded up.
• A004222 (program): 100*log_10 (n) rounded down.
• A004223 (program): 100*log_10 (n) rounded to nearest integer.
• A004224 (program): 100*log_10 (n) rounded up.
• A004232 (program): a(n) = n^2 + prime(n).
• A004233 (program): a(n) = ceiling(log(n)).
• A004235 (program): 10*log(n) rounded to nearest integer.
• A004236 (program): a(n) = ceiling(10*log(n)).
• A004239 (program): a(n) = ceiling(100*log(n)).
• A004247 (program): Multiplication table read by antidiagonals: T(i,j) = i*j (i>=0, j>=0). Alternatively, multiplication triangle read by rows: P(i,j) = j*(i-j) (i>=0, 0<=j<=i).
• A004248 (program): Table of x^y, where (x,y) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), …
• A004250 (program): Number of partitions of n into 3 or more parts.
• A004253 (program): a(n) = 5*a(n-1) - a(n-2), with a(1)=1, a(2)=4.
• A004254 (program): a(n) = 5*a(n-1) - a(n-2) for n > 1, a(0) = 0, a(1) = 1.
• A004255 (program): n(n+1)(n^2 -3n + 6)/8.
• A004256 (program): a(n) = n^2*(n+1)*(n+2)^2/6.
• A004257 (program): a(n) = round(log_2(n)).
• A004259 (program): a(n) = floor(10*log_2(n)).
• A004260 (program): a(n) = round(10*log_2(n)).
• A004261 (program): a(n) = ceiling(10*log_2(n)).
• A004262 (program): a(n) = floor(100*log_2(n)).
• A004263 (program): a(n) = round(100*log_2(n)).
• A004264 (program): a(n) = ceiling(100*log_2(n)).
• A004271 (program): 1, 3 and the nonnegative even numbers.
• A004272 (program): 1, 3, 5 and the even numbers.
• A004273 (program): 0 together with odd numbers.
• A004274 (program): 0, 2 and the odd numbers.
• A004275 (program): 1 together with nonnegative even numbers.
• A004276 (program): 0, 2, 4 and the odd numbers.
• A004277 (program): 1 together with positive even numbers.
• A004278 (program): 1, 3 and the positive even numbers.
• A004279 (program): 1, 3, 5 and the even numbers.
• A004280 (program): 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes).
• A004281 (program): 2, 4 and the odd numbers.
• A004282 (program): a(n) = n*(n+1)^2*(n+2)^2/12.
• A004283 (program): Least positive multiple of n written in base 3 using only 0 and 1.
• A004291 (program): Expansion of (1 + 2*x + x^2)/(1 - 10*x + x^2).
• A004292 (program): Expansion of (1+x)^2/(1-18*x+x^2).
• A004293 (program): Expansion of (1+2*x+x^2)/(1-26*x+x^2).
• A004294 (program): Expansion of (1+2*x+x^2)/(1-34*x+x^2).
• A004295 (program): Expansion of (1+2*x+x^2)/(1-42*x+x^2).
• A004296 (program): Expansion of (1+2*x+x^2)/(1-50*x+x^2).
• A004297 (program): Expansion of (1+2*x+x^2)/(1-58*x+x^2).
• A004298 (program): Expansion of (1+2*x+x^2)/(1-66*x+x^2).
• A004299 (program): Expansion of (1+2*x+x^2)/(1-74*x+x^2).
• A004301 (program): Second-order Eulerian numbers «n,2».
• A004302 (program): a(n) = n^2*(n+1)^2*(n+2)/12.
• A004303 (program): a(n) = C(2n-2,n-1)/n - 2^(n-1) + n.
• A004305 (program): Simple triangulations of a disk: column 4 of square array in A210664.
• A004310 (program): Binomial coefficient C(2n,n-4).
• A004311 (program): Binomial coefficient C(2n,n-5).
• A004312 (program): Binomial coefficient C(2n,n-6).
• A004313 (program): a(n) = binomial coefficient C(2n, n-7).
• A004314 (program): a(n) = binomial coefficient C(2n, n - 8).
• A004315 (program): a(n) = binomial coefficient C(2n, n-9).
• A004316 (program): a(n) = binomial coefficient C(2n, n-10).
• A004317 (program): Binomial coefficient C(2n,n-11).
• A004318 (program): Binomial coefficient C(2n,n-12).
• A004319 (program): Binomial coefficient C(3n,n-1).
• A004320 (program): a(n) = n*(n+1)*(n+2)^2/6.
• A004321 (program): Binomial coefficient C(3n, n-3).
• A004322 (program): Binomial coefficient C(3n,n-4).
• A004323 (program): Binomial coefficient C(3n,n-5).
• A004324 (program): Binomial coefficient C(3n,n-6).
• A004325 (program): Binomial coefficient C(3n,n-7).
• A004326 (program): Binomial coefficient C(3n,n-8).
• A004327 (program): Binomial coefficient C(3n,n-9).
• A004328 (program): Binomial coefficient C(3n,n-10).
• A004329 (program): Binomial coefficient C(3n,n-11).
• A004330 (program): Binomial coefficient C(3n,n-12).
• A004331 (program): Binomial coefficient C(4n,n-1).
• A004332 (program): a(n) = C(4n,n-2).
• A004333 (program): Binomial coefficient C(4n,n-3).
• A004334 (program): Binomial coefficient C(4n,n-4).
• A004335 (program): Binomial coefficient C(4n,n-5).
• A004336 (program): Binomial coefficient C(4n,n-6).
• A004337 (program): Binomial coefficient C(4n,n-7).
• A004338 (program): Binomial coefficient C(4n,n-8).
• A004339 (program): Binomial coefficient C(4n,n-9).
• A004340 (program): Binomial coefficient C(4n,n-10).
• A004341 (program): Binomial coefficient C(4n,n-11).
• A004342 (program): Binomial coefficient C(4n, n-12).
• A004343 (program): Binomial coefficient C(5n,n-1).
• A004344 (program): Binomial coefficient C(5n+10,n).
• A004345 (program): Binomial coefficient C(5n,n-3).
• A004346 (program): Binomial coefficient C(5n,n-4).
• A004347 (program): Binomial coefficient C(5n,n-5).
• A004348 (program): Binomial coefficient C(5n, n-6).
• A004349 (program): Binomial coefficient C(5n,n-7).
• A004350 (program): Binomial coefficient C(5n,n-8).
• A004351 (program): Binomial coefficient C(5*n,n-9).
• A004352 (program): Binomial coefficient C(5n,n-10).
• A004353 (program): Binomial coefficient C(5n,n-11).
• A004354 (program): Binomial coefficient C(5n, n-12).
• A004355 (program): Binomial coefficient C(6n,n).
• A004356 (program): Binomial coefficient C(6n,n-1).
• A004357 (program): a(n) = binomial(6*n,n-2).
• A004358 (program): Binomial coefficient C(6n,n-3).
• A004359 (program): Binomial coefficient C(6n,n-4).
• A004360 (program): Binomial coefficient C(6n,n-5).
• A004361 (program): Binomial coefficient C(6n,n-6).
• A004362 (program): Binomial coefficient C(6n,n-7).
• A004363 (program): Binomial coefficient C(6n,n-8).
• A004364 (program): Binomial coefficient C(6n,n-9).
• A004365 (program): Binomial coefficient C(6n,n-10).
• A004366 (program): Binomial coefficient C(6n,n-11).
• A004367 (program): Binomial coefficient C(6n,n-12).
• A004368 (program): Binomial coefficient C(7n,n).
• A004369 (program): Binomial coefficient C(7n,n-1).
• A004370 (program): Binomial coefficient C(7n,n-2).
• A004371 (program): Binomial coefficient C(7n,n-3).
• A004372 (program): Binomial coefficient C(7n,n-4).
• A004373 (program): Binomial coefficient C(7n,n-5).
• A004374 (program): Binomial coefficient C(7n,n-6).
• A004375 (program): Binomial coefficient C(7n,n-7).
• A004376 (program): Binomial coefficient C(7n,n-8).
• A004377 (program): Binomial coefficient C(7n,n-9).
• A004378 (program): Binomial coefficient C(7n,n-10).
• A004379 (program): Binomial coefficient C(7n,n-11).
• A004380 (program): Binomial coefficient C(7n,n-12).
• A004381 (program): Binomial coefficient C(8n,n).
• A004382 (program): Binomial coefficient C(8n, n-1).
• A004383 (program): Binomial coefficient C(8n,n-2).
• A004384 (program): Binomial coefficient C(8n,n-3).
• A004385 (program): Binomial coefficient C(8n,n-4).
• A004386 (program): Binomial coefficient C(8n,n-5).
• A004387 (program): Binomial coefficient C(8n,n-6).
• A004388 (program): Binomial coefficient C(8n,n-7).
• A004389 (program): a(n) = binomial(8*n, n-8).
• A004390 (program): Binomial coefficient C(8n,n-9).
• A004391 (program): Binomial coefficient C(8n,n-10).
• A004392 (program): Binomial coefficient C(8n,n-11).
• A004393 (program): Binomial coefficient C(8n,n-12).
• A004395 (program): Ratios of successive terms are 1,1,2,3,3,4,5,5,6,7,7,…
• A004396 (program): One even number followed by two odd numbers.
• A004397 (program): a(n) = prime(n) + Fibonacci(n).
• A004398 (program): a(n) = Fibonacci(n+1) + prime(n).
• A004399 (program): Fibonacci(n+2) plus n-th prime.
• A004400 (program): a(n) = 1 + Sum_{k=0..n} 2^k*k!.
• A004401 (program): Least number of edges in graph containing all trees on n nodes.
• A004402 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-1).
• A004403 (program): Expansion of 1/theta_3(q)^2 in powers of q.
• A004404 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-3).
• A004405 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-4).
• A004406 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-5).
• A004407 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-6).
• A004408 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).
• A004409 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-8).
• A004410 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-9).
• A004411 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-10).
• A004412 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-11).
• A004413 (program): Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-12).
• A004414 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-13).
• A004415 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-14).
• A004416 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15).
• A004417 (program): Expansion of (Sum x^(n^2), n = -inf .. inf )^(-16).
• A004418 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-17).
• A004419 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-18).
• A004420 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-19).
• A004421 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-20).
• A004422 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-21).
• A004423 (program): Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-22).
• A004425 (program): Expansion of (Sum x^(n^2), n = -inf .. inf )^(-24).
• A004426 (program): Arithmetic mean of digits of n (rounded down).
• A004427 (program): Arithmetic mean of digits of n (rounded up).
• A004431 (program): Numbers that are the sum of 2 distinct nonzero squares.
• A004435 (program): Positive integers that are not the sum of 2 distinct square integers.
• A004439 (program): Numbers that are not the sum of 2 distinct nonzero squares.
• A004442 (program): Natural numbers, pairs reversed: a(n) = n + (-1)^n; also Nimsum n + 1.
• A004443 (program): Nimsum n + 2.
• A004444 (program): Nimsum n + 3.
• A004445 (program): Nimsum n + 4.
• A004446 (program): a(n) = Nimsum n + 5.
• A004447 (program): Nimsum n + 6.
• A004448 (program): Nimsum n + 7.
• A004449 (program): Nimsum n + 8.
• A004450 (program): Nimsum n + 9.
• A004451 (program): Nimsum n + 10.
• A004452 (program): Nimsum n + 11.
• A004453 (program): Nimsum n + 12.
• A004454 (program): Nimsum n + 13.
• A004455 (program): Nimsum n + 14.
• A004456 (program): Nimsum n + 15.
• A004457 (program): Nimsum n + 16.
• A004458 (program): Nimsum n + 17.
• A004459 (program): Nimsum n + 18.
• A004460 (program): Nimsum n + 19.
• A004461 (program): Nimsum n + 20.
• A004462 (program): Nimsum n + 21.
• A004463 (program): Nimsum n + 22.
• A004464 (program): Nimsum n + 23.
• A004465 (program): Nimsum n + 24.
• A004466 (program): a(n) = n*(5*n^2 - 2)/3.
• A004467 (program): a(n) = n*(11*n^2 - 5)/6.
• A004468 (program): a(n) = Nim product 3 * n.
• A004482 (program): Tersum n + 1 (answer recorded in base 10).
• A004483 (program): Tersum n + 2.
• A004488 (program): Tersum n + n.
• A004492 (program): Tersum n + 3.
• A004493 (program): Tersum n + 4.
• A004494 (program): Tersum n + 5.
• A004495 (program): Tersum n + 6.
• A004496 (program): Tersum n + 7.
• A004497 (program): Tersum n + 8.
• A004498 (program): Tersum n + 9.
• A004499 (program): Tersum n + 10.
• A004500 (program): Tersum n + 11.
• A004501 (program): Tersum n + 12.
• A004502 (program): Tersum n + 13.
• A004503 (program): Tersum n + 14.
• A004504 (program): Tersum n + 15.
• A004505 (program): Tersum n + 16.
• A004506 (program): Tersum n + 17.
• A004507 (program): Tersum n + 18.
• A004508 (program): Tersum n + 19.
• A004509 (program): Tersum n + 20.
• A004510 (program): Tersum n + 21.
• A004511 (program): Tersum n + 22.
• A004512 (program): Tersum n + 23.
• A004513 (program): Tersum n + 24.
• A004514 (program): Generalized nim sum n + n in base 4.
• A004515 (program): Generalized nim sum n + n in base 5.
• A004516 (program): Generalized nim sum n + n in base 6.
• A004517 (program): Generalized nim sum n + n in base 7.
• A004518 (program): Generalized nim sum n + n in base 8.
• A004519 (program): Generalized nim sum n + n in base 9.
• A004520 (program): Generalized nim sum n + n in base 10.
• A004521 (program): Generalized nim sum n + n in base 11.
• A004522 (program): Generalized nim sum n + n in base 12.
• A004523 (program): Two even followed by one odd; or floor(2n/3).
• A004524 (program): Three even followed by one odd.
• A004525 (program): One even followed by three odd.
• A004526 (program): Nonnegative integers repeated, floor(n/2).
• A004527 (program): Ratios of successive terms are 1,2,2,3,4,4,5,6,6,…
• A004528 (program): Ratios of successive terms are 1,2,2,2,3,4,4,4,5,6,6,6,7…
• A004529 (program): Ratios of successive terms are 1,1,1,2,3,3,3,4,5,5,5,6,…
• A004531 (program): Number of integer solutions to x^2 + 4 * y^2 = n.
• A004538 (program): a(n) = 3*n^2 + 3*n - 1.
• A004539 (program): Expansion of sqrt(2) in base 2.
• A004540 (program): Expansion of sqrt(2) in base 3.
• A004541 (program): Expansion of sqrt(2) in base 4.
• A004542 (program): Expansion of sqrt(2) in base 5.
• A004543 (program): Expansion of sqrt(2) in base 6.
• A004544 (program): Expansion of sqrt(2) in base 7.
• A004545 (program): Expansion of sqrt(2) in base 8.
• A004546 (program): Expansion of sqrt(2) in base 9.
• A004547 (program): Expansion of sqrt(3) in base 2.
• A004548 (program): Expansion of sqrt(3) in base 3.
• A004549 (program): Expansion of sqrt(3) in base 4.
• A004550 (program): Expansion of sqrt(3) in base 5.
• A004551 (program): Expansion of sqrt(3) in base 6.
• A004552 (program): Expansion of sqrt(3) in base 7.
• A004553 (program): Expansion of sqrt(3) in base 8.
• A004554 (program): Expansion of sqrt(3) in base 9.
• A004555 (program): Expansion of sqrt(5) in base 2.
• A004556 (program): Expansion of sqrt(5) in base 3.
• A004557 (program): Expansion of sqrt(5) in base 4.
• A004558 (program): Expansion of sqrt(5) in base 5.
• A004559 (program): Expansion of sqrt(5) in base 6.
• A004560 (program): Expansion of sqrt(5) in base 7.
• A004561 (program): Expansion of sqrt(5) in base 8.
• A004562 (program): Expansion of sqrt(5) in base 9.
• A004563 (program): Expansion of sqrt(6) in base 4.
• A004564 (program): Expansion of sqrt(6) in base 5.
• A004565 (program): Expansion of sqrt(6) in base 6.
• A004566 (program): Expansion of sqrt(6) in base 7.
• A004567 (program): Expansion of sqrt(6) in base 8.
• A004568 (program): Expansion of sqrt(6) in base 9.
• A004569 (program): Expansion of sqrt(7) in base 2.
• A004570 (program): Expansion of sqrt(7) in base 3.
• A004571 (program): Expansion of sqrt(7) in base 4.
• A004572 (program): Expansion of sqrt(7) in base 5.
• A004573 (program): Expansion of sqrt(7) in base 6.
• A004574 (program): Expansion of sqrt(7) in base 7.
• A004575 (program): Expansion of sqrt(7) in base 8.
• A004576 (program): Expansion of sqrt(7) in base 9.
• A004578 (program): Expansion of sqrt(8) in base 3.
• A004579 (program): Expansion of sqrt(8) in base 4.
• A004580 (program): Expansion of sqrt(8) in base 5.
• A004581 (program): Expansion of sqrt(8) in base 6.
• A004582 (program): Expansion of sqrt(8) in base 7.
• A004583 (program): Expansion of sqrt(8) in base 8.
• A004584 (program): Expansion of sqrt(8) in base 9.
• A004585 (program): Expansion of sqrt(10) in base 2.
• A004586 (program): Expansion of sqrt(10) in base 3.
• A004587 (program): Expansion of sqrt(10) in base 4.
• A004588 (program): Expansion of sqrt(10) in base 5.
• A004589 (program): Expansion of sqrt(10) in base 6.
• A004590 (program): Expansion of sqrt(10) in base 7.
• A004591 (program): Expansion of sqrt(10) in base 8.
• A004592 (program): Expansion of sqrt(10) in base 9.
• A004593 (program): Expansion of e in base 2.
• A004595 (program): Expansion of e in base 4.
• A004596 (program): Expansion of e in base 5.
• A004599 (program): Expansion of e in base 8.
• A004601 (program): Expansion of Pi in base 2 (or, binary expansion of Pi).
• A004603 (program): Expansion of Pi in base 4.
• A004604 (program): Expansion of Pi in base 5.
• A004609 (program): Expansion of sqrt(6) in base 2.
• A004610 (program): Expansion of sqrt(6) in base 3.
• A004611 (program): Divisible only by primes congruent to 1 mod 3.
• A004612 (program): Numbers that are divisible only by primes congruent to 2 mod 3.
• A004613 (program): Numbers that are divisible only by primes congruent to 1 mod 4.
• A004614 (program): Numbers that are divisible only by primes congruent to 3 mod 4.
• A004625 (program): Numbers divisible only by primes congruent to 1 mod 8.
• A004630 (program): Squares written in base 12. (Next term contains a non-decimal character.)
• A004631 (program): Squares written in base 16. (Next term contains a non-decimal character.)
• A004632 (program): Cubes written in base 2.
• A004633 (program): Cubes written in base 3.
• A004634 (program): Cubes written in base 4.
• A004635 (program): Cubes written in base 5.
• A004636 (program): Cubes written in base 6.
• A004637 (program): Cubes written in base 7.
• A004638 (program): Cubes written in base 8.
• A004639 (program): Cubes written in base 9.
• A004641 (program): Fixed under 0 -> 10, 1 -> 100.
• A004642 (program): Powers of 2 written in base 3.
• A004643 (program): Powers of 2 written in base 4.
• A004645 (program): Powers of 2 written in base 6.
• A004646 (program): Powers of 2 written in base 7.
• A004647 (program): Powers of 2 written in base 8.
• A004648 (program): a(n) = prime(n) mod n.
• A004649 (program): Prime(n) mod (n-1).
• A004650 (program): Prime(n) mod (n+1).
• A004652 (program): Expansion of x*(1+x^2+x^4)/((1-x)*(1-x^2)*(1-x^3)).
• A004654 (program): Powers of 2 written in base 15. (Next term contains a non-decimal character.)
• A004655 (program): Powers of 2 written in base 16.
• A004656 (program): Powers of 3 written in base 2.
• A004657 (program): Expansion of g.f.: (1+x^3)*(1+x^4)/((1-x)*(1-x^2)^2*(1-x^4)).
• A004658 (program): Powers of 3 written in base 4.
• A004659 (program): Powers of 3 written in base 5.
• A004660 (program): Powers of 3 written in base 6.
• A004661 (program): Powers of 3 written in base 7.
• A004662 (program): Powers of 3 written in base 8.
• A004663 (program): Powers of 3 written in base 9.
• A004664 (program): n! + n^2.
• A004669 (program): Powers of 3 written in base 27.
• A004676 (program): Primes written in base 2.
• A004678 (program): Primes written in base 4.
• A004679 (program): Primes written in base 5.
• A004680 (program): Primes written in base 6.
• A004681 (program): Primes written in base 7.
• A004682 (program): Primes written in base 8.
• A004683 (program): Primes written in base 9.
• A004684 (program): Primes written in base 11. (Next term contains a nondecimal character.)
• A004685 (program): Fibonacci numbers written in base 2.
• A004686 (program): Fibonacci numbers written in base 3.
• A004687 (program): Fibonacci numbers written in base 4.
• A004688 (program): Fibonacci numbers written in base 5.
• A004689 (program): Fibonacci numbers written in base 6.
• A004690 (program): Fibonacci numbers written in base 7.
• A004691 (program): Fibonacci numbers written in base 8.
• A004692 (program): Fibonacci numbers written in base 9.
• A004694 (program): Fibonacci numbers written in base 13. (Next term contains a non-decimal character).
• A004695 (program): a(n) = floor(Fibonacci(n)/2).
• A004696 (program): a(n) = floor(Fibonacci(n)/3).
• A004697 (program): a(n) = floor(Fibonacci(n)/4).
• A004698 (program): a(n) = floor(Fibonacci(n)/5).
• A004699 (program): a(n) = floor(Fibonacci(n)/6).
• A004700 (program): Expansion of e.g.f. 1/(3 - exp(x) - exp(2*x)).
• A004709 (program): Cubefree numbers: numbers that are not divisible by any cube > 1.
• A004711 (program): Positions of 1’s in binary expansion of Pi/4.
• A004712 (program): Positions of ones in binary expansion of e-2.
• A004713 (program): Positions of ones in binary expansion of 1/sqrt(2).
• A004714 (program): Positions of ones in binary expansion of the reciprocal of the golden ratio (0.618…).
• A004718 (program): The Danish composer Per Nørgård’s “infinity sequence”, invented in an attempt to unify in a perfect way repetition and variation: a(2n) = -a(n), a(2n+1) = a(n) + 1, a(0) = 0.
• A004719 (program): Delete all 0’s from n.
• A004727 (program): Delete all 8’s from the sequence of nonnegative integers.
• A004728 (program): Delete all 9’s from the sequence of nonnegative integers.
• A004729 (program): Divisors of 2^32 - 1 (for a(1) to a(31), the 31 regular polygons with an odd number of sides constructible with ruler and compass).
• A004730 (program): Numerator of n!!/(n+1)!! (cf. A006882).
• A004731 (program): Denominator of n!!/(n+1)!! (cf. A006882).
• A004732 (program): Numerator of n!!/(n+3)!!.
• A004733 (program): Denominator of n!!/(n+3)!!.
• A004734 (program): Numerator of average distance traveled by n-dimensional fly.
• A004735 (program): Denominator of average distance traveled by n-dimensional fly.
• A004736 (program): Triangle read by rows: row n lists the first n positive integers in decreasing order.
• A004737 (program): Concatenation of sequences (1,2,…,n-1,n,n-1,…,1) for n >= 1.
• A004738 (program): Concatenation of sequences (1,2,…,n-1,n,n-1,…,2) for n >= 2.
• A004739 (program): Concatenation of sequences (1,2,2,…,n-1,n-1,n,n,n-1,n-1,…,2,2,1) for n >= 1.
• A004741 (program): Concatenation of sequences (1,3,..,2n-1,2n,2n-2,..,2) for n >= 1.
• A004742 (program): Numbers whose binary expansion does not contain 101.
• A004743 (program): Numbers whose binary expansion does not contain 110.
• A004745 (program): Numbers whose binary expansion does not contain 001.
• A004746 (program): Numbers whose binary expansion does not contain 010.
• A004748 (program): Binary expansion contains 101.
• A004749 (program): Numbers whose binary expansion contains the substring ‘110’.
• A004751 (program): Binary expansion contains 001.
• A004752 (program): Binary expansion contains 010.
• A004753 (program): Numbers whose binary expansion contains 100.
• A004754 (program): Numbers n whose binary expansion starts 10.
• A004755 (program): Binary expansion starts 11.
• A004756 (program): Binary expansion starts 100.
• A004757 (program): Binary expansion starts 101.
• A004758 (program): Binary expansion starts 110.
• A004759 (program): Binary expansion starts 111.
• A004760 (program): List of numbers whose binary expansion does not begin 10.
• A004761 (program): Numbers n whose binary expansion does not begin with 11.
• A004762 (program): Numbers whose binary expansion does not begin 100.
• A004763 (program): Numbers whose binary expansion does not begin 101.
• A004764 (program): Numbers whose binary expansion does not begin 110.
• A004765 (program): Numbers whose binary expansion does not begin 111.
• A004766 (program): Numbers whose binary expansion ends 01.
• A004767 (program): a(n) = 4*n + 3.
• A004768 (program): Binary expansion ends 001.
• A004769 (program): Numbers whose binary expansion ends in 011.
• A004770 (program): Numbers of form 8n+5; or, numbers whose binary expansion ends in 101.
• A004771 (program): a(n) = 8*n + 7. Or, numbers whose binary expansion ends in 111.
• A004772 (program): Numbers that are not congruent to 1 (mod 4).
• A004773 (program): Numbers congruent to {0, 1, 2} mod 4: a(n) = floor(4*n/3).
• A004774 (program): Numbers n whose binary expansion does not end in 001.
• A004775 (program): Numbers k such that the binary expansion of k does not end in 011.
• A004776 (program): Numbers not congruent to 5 (mod 8).
• A004777 (program): Numbers not congruent to 7 mod 8.
• A004779 (program): Binary expansion contains 3 adjacent 0’s.
• A004780 (program): Binary expansion contains 2 adjacent 1’s.
• A004781 (program): Binary expansion contains 3 adjacent 1’s.
• A004782 (program): 2(2n-3)!/n!(n-1)! is an integer.
• A004783 (program): 3!(2n-4)!/n!(n-1)! is an integer.
• A004788 (program): Number of distinct prime divisors of the numbers in row n of Pascal’s triangle.
• A004793 (program): a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), …, a(n-1), k form an arithmetic progression.
• A004797 (program): Convolution of A002024 with itself.
• A004798 (program): Convolution of Fibonacci numbers 1,2,3,5,… with themselves.
• A004799 (program): Self-convolution of Lucas numbers.
• A004825 (program): Numbers that are the sum of at most 3 positive cubes.
• A004826 (program): Numbers that are the sum of at most 4 positive cubes.
• A004827 (program): Numbers that are the sum of at most 5 positive cubes.
• A004870 (program): Numbers that are the sum of at most 8 positive 7th powers.
• A004872 (program): Numbers that are the sum of at most 10 positive 7th powers.
• A004873 (program): Numbers that are the sum of at most 11 positive 7th powers.
• A004874 (program): Numbers that are the sum of at most 12 positive 7th powers.
• A004886 (program): Numbers that are the sum of at most 2 positive 9th powers.
• A004891 (program): Numbers that are the sum of at most 7 positive 9th powers.
• A004892 (program): Numbers that are the sum of at most 8 positive 9th powers.
• A004894 (program): Numbers that are the sum of at most 10 positive 9th powers.
• A004895 (program): Numbers that are the sum of at most 11 positive 9th powers.
• A004896 (program): Numbers that are the sum of at most 12 positive 9th powers.
• A004897 (program): Numbers that are the sum of at most 2 nonzero 10th powers.
• A004902 (program): Numbers that are the sum of at most 7 nonzero 10th powers.
• A004903 (program): Numbers that are the sum of at most 8 nonzero 10th powers.
• A004906 (program): Numbers that are the sum of at most 11 nonzero 10th powers.
• A004907 (program): Numbers that are the sum of at most 12 nonzero 10th powers.
• A004908 (program): Numbers that are the sum of at most 2 positive 11th powers.
• A004919 (program): a(n) = floor(n*phi^4), where phi is the golden ratio, A001622.
• A004920 (program): Floor of n*phi^5, where phi is the golden ratio, A001622.
• A004921 (program): Floor of n*phi^6, phi = golden ratio, A001622.
• A004922 (program): Floor of n*phi^7, where phi is the golden ratio, A001622.
• A004923 (program): Floor of n*phi^8, where phi is the golden ratio, A001622.
• A004924 (program): Floor of n*phi^9, where phi is the golden ratio, A001622.
• A004925 (program): Floor of n*phi^10, where phi is the golden ratio, A001622.
• A004926 (program): Floor of n*phi^11, where phi is the golden ratio, A001622.
• A004927 (program): Floor of n*phi^12, where phi is the golden ratio, A001622.
• A004928 (program): Floor of n*phi^13, where phi is the golden ratio, A001622.
• A004929 (program): Floor of n*phi^14, where phi is the golden ratio, A001622.
• A004930 (program): Floor of n*phi^15, where phi is the golden ratio, A001622.
• A004931 (program): Floor of n*phi^16, where phi is the golden ratio, A001622.
• A004932 (program): Floor of n*phi^17, where phi is the golden ratio, A001622.
• A004933 (program): Floor of n*phi^18, where phi is the golden ratio, A001622.
• A004934 (program): Floor of n*phi^19, where phi is the golden ratio, A001622.
• A004935 (program): Floor of n*phi^20, where phi is the golden ratio, A001622.
• A004936 (program): Numerator of (binomial(2*n-2,n-1)/n!)^2.
• A004937 (program): Nearest integer to n*phi^2, where phi is the golden ratio, A001622.
• A004938 (program): Nearest integer to n*phi^3, where phi is the golden ratio, A001622.
• A004939 (program): Nearest integer to n*phi^4, where phi is the golden ratio, A001622.
• A004940 (program): Nearest integer to n*phi^5, where phi is the golden ratio, A001622.
• A004941 (program): Nearest integer to n*phi^6, where phi is the golden ratio, A001622.
• A004942 (program): Nearest integer to n*phi^7, where phi is the golden ratio, A001622.
• A004943 (program): Nearest integer to n*phi^8, where phi is the golden ratio, A001622.
• A004944 (program): Nearest integer to n*phi^9, where phi is the golden ratio, A001622.
• A004945 (program): Nearest integer to n*phi^10, where phi is the golden ratio, A001622.
• A004946 (program): Nearest integer to n*phi^11, where phi is the golden ratio, A001622.
• A004947 (program): Nearest integer to n*phi^12, where phi is the golden ratio, A001622.
• A004948 (program): Nearest integer to n*phi^13, where phi is the golden ratio, A001622.
• A004949 (program): Nearest integer to n*phi^14, where phi is the golden ratio, A001622.
• A004950 (program): Nearest integer to n*phi^15, where phi is the golden ratio, A001622.
• A004951 (program): Nearest integer to n*phi^16, where phi is the golden ratio, A001622.
• A004952 (program): Nearest integer to n*phi^17, where phi is the golden ratio, A001622.
• A004953 (program): Nearest integer to n*phi^18, where phi is the golden ratio, A001622.
• A004954 (program): Nearest integer to n*phi^19, where phi is the golden ratio, A001622.
• A004955 (program): Nearest integer to n*phi^20, where phi is the golden ratio, A001622.
• A004956 (program): a(n) = ceiling(n*phi), where phi is the golden ratio, A001622.
• A004957 (program): a(n) = ceiling(n*phi^2), where phi is the golden ratio, A001622.
• A004958 (program): a(n) = ceiling(n*phi^3), where phi is the golden ratio, A001622.
• A004959 (program): a(n) = ceiling(n*phi^4), where phi is the golden ratio, A001622.
• A004960 (program): a(n) = ceiling(n*phi^5), where phi is the golden ratio, A001622.
• A004961 (program): a(n) = ceiling(n*phi^6), where phi is the golden ratio.
• A004962 (program): a(n) = ceiling(n*phi^7), where phi is the golden ratio, A001622.
• A004963 (program): a(n) = ceiling(n*phi^8), where phi is the golden ratio, A001622.
• A004964 (program): a(n) = ceiling(n*phi^9), where phi is the golden ratio, A001622.
• A004965 (program): a(n) = ceiling(n*phi^10), where phi is the golden ratio, A001622.
• A004966 (program): a(n) = ceiling(n*phi^11), where phi is the golden ratio, A001622.
• A004967 (program): a(n) = ceiling(n*phi^12), where phi is the golden ratio, A001622.
• A004968 (program): a(n) = ceiling(n*phi^13), where phi is the golden ratio, A001622.
• A004969 (program): a(n) = ceiling(n*phi^14), where phi is the golden ratio, A001622.
• A004970 (program): a(n) = ceiling(n*phi^15), where phi is the golden ratio, A001622.
• A004971 (program): a(n) = ceiling(n*phi^16), where phi is the golden ratio, A001622.
• A004972 (program): a(n) = ceiling(n*phi^17), where phi is the golden ratio, A001622.
• A004973 (program): a(n) = ceiling(n*phi^18), where phi is the golden ratio, A001622.
• A004974 (program): a(n) = ceiling(n*phi^19), where phi is the golden ratio, A001622.
• A004975 (program): a(n) = ceiling(n*phi^20), where phi is the golden ratio, A001622.
• A004976 (program): a(n) = floor(n*phi^3), where phi=(1+sqrt(5))/2.
• A004981 (program): a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k + 1).
• A004982 (program): a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k + 3).
• A004983 (program): a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k - 3).
• A004984 (program): a(n) = (2^n/n!)*Product_{k=0..n-1} (4*k - 1).
• A004985 (program): a(n) = (2^n/n!)*Product_{k=0..n-1} (4*k + 5).
• A004986 (program): a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k + 7).
• A004987 (program): a(n) = (3^n/n!)*Product_{k=0..n-1} (3*k + 1).
• A004988 (program): a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k + 2).
• A004989 (program): a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k - 2).
• A004990 (program): a(n) = (3^n/n!)*Product_{k=0..n-1}(3*k - 1).
• A004991 (program): a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k + 4).
• A004992 (program): a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k + 5).
• A004993 (program): a(n) = (6^n/n!)*Product_{k=0..n-1} (6*k + 1).
• A004994 (program): a(n) = (6^n/n!)*Product_{k=0..n-1} (6*k + 5).
• A004995 (program): a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k - 5).
• A004996 (program): a(n) = 6^n/n! * Product_{k=0..n-1} (6*k - 1).
• A004997 (program): a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k + 7).
• A004998 (program): a(n) = (6^n/n!) * Product_{k=0..n-1} ( 6*k + 11 ).
• A004999 (program): Sums of two nonnegative cubes.
• A005001 (program): a(0) = 0; for n>0, a(n) = Sum_k={0..n-1} Bell(k), where the Bell numbers Bell(k) are given in A000110.
• A005002 (program): Number of rhyme schemes (see reference for precise definition).
• A005003 (program): Number of rhyme schemes (see reference for precise definition).
• A005004 (program): Davenport-Schinzel numbers of degree n on 3 symbols.
• A005005 (program): Davenport-Schinzel numbers of degree n on 4 symbols.
• A005006 (program): Davenport-Schinzel numbers of degree n on 5 symbols.
• A005008 (program): a(n) = n! - n^2.
• A005009 (program): a(n) = 7*2^n.
• A005010 (program): a(n) = 9*2^n.
• A005011 (program): Shifts one place left under 5th-order binomial transform.
• A005012 (program): Shifts one place left under 6th-order binomial transform.
• A005013 (program): a(n) = 3*a(n-2) - a(n-4), a(0)=0, a(1)=1, a(2)=1, a(3)=4. Alternates Fibonacci (A000045) and Lucas (A000032) sequences for even and odd n.
• A005014 (program): Certain subgraphs of a directed graph (inverse binomial transform of A005321).
• A005015 (program): a(n) = 11*2^n.
• A005016 (program): Certain subgraphs of a directed graph.
• A005017 (program): Denominator of (binomial(2*n-2,n-1)/n!)^2.
• A005019 (program): The number of n X n (0,1)-matrices with a 1-width of 1.
• A005021 (program): Random walks (binomial transform of A006054).
• A005022 (program): Number of walks of length 2n+6 in the path graph P_7 from one end to the other.
• A005023 (program): Number of walks of length 2n+7 in the path graph P_8 from one end to the other.
• A005024 (program): Number of walks of length 2n+8 in the path graph P_9 from one end to the other.
• A005025 (program): Random walks.
• A005029 (program): 13*2^n.
• A005030 (program): a(n) = 5*3^n.
• A005032 (program): a(n) = 7*3^n.
• A005041 (program): A self-generating sequence.
• A005043 (program): Riordan numbers: a(n) = (n-1)*(2*a(n-1) + 3*a(n-2))/(n+1).
• A005044 (program): Alcuin’s sequence: expansion of x^3/((1-x^2)*(1-x^3)*(1-x^4)).
• A005045 (program): Number of restricted 3 X 3 matrices with row and column sums n.
• A005046 (program): Number of partitions of a 2n-set into even blocks.
• A005051 (program): a(n) = 8*3^n.
• A005052 (program): 10*3^n.
• A005053 (program): Expand (1-2*x)/(1-5*x).
• A005054 (program): a(0) = 1; a(n) = 4*5^(n-1) for n >= 1.
• A005055 (program): 7*5^n.
• A005056 (program): a(n) = 3^n + 2^n - 1.
• A005057 (program): a(n) = 5^n - 2^n.
• A005058 (program): a(n) = 5^n - 3^n.
• A005059 (program): a(n) = (5^n - 3^n)/2.
• A005060 (program): a(n) = 5^n - 4^n.
• A005061 (program): a(n) = 4^n - 3^n.
• A005062 (program): a(n) = 6^n - 5^n.
• A005063 (program): Sum of squares of primes dividing n.
• A005064 (program): Sum of cubes of primes dividing n.
• A005065 (program): Sum of 4th powers of primes dividing n.
• A005066 (program): Sum of squares of odd primes dividing n.
• A005067 (program): Sum of cubes of odd primes dividing n.
• A005068 (program): Sum of 4th powers of odd primes dividing n.
• A005069 (program): Sum of odd primes dividing n.
• A005070 (program): Sum of primes = 1 (mod 3) dividing n.
• A005073 (program): Sum of 4th powers of primes = 1 mod 3 dividing n.
• A005074 (program): Sum of primes = 2 mod 3 dividing n.
• A005075 (program): Sum of squares of primes = 2 mod 3 dividing n.
• A005076 (program): Sum of cubes of primes = 2 mod 3 dividing n.
• A005077 (program): Sum of 4th powers of primes = 2 mod 3 dividing n.
• A005078 (program): Sum of primes = 1 mod 4 dividing n.
• A005079 (program): Sum of squares of primes = 1 mod 4 dividing n.
• A005080 (program): Sum of cubes of primes = 1 mod 4 dividing n.
• A005081 (program): Sum of 4th powers of primes = 1 mod 4 dividing n.
• A005082 (program): Sum of primes = 3 mod 4 dividing n.
• A005083 (program): Sum of squares of primes = 3 mod 4 dividing n.
• A005084 (program): Sum of cubes of primes = 3 mod 4 dividing n.
• A005085 (program): Sum of 4th powers of primes = 3 mod 4 dividing n.
• A005086 (program): Number of Fibonacci numbers 1,2,3,5,… dividing n.
• A005087 (program): Number of distinct odd primes dividing n.
• A005088 (program): Number of primes = 1 mod 3 dividing n.
• A005089 (program): Number of distinct primes == 1 (mod 4) dividing n.
• A005090 (program): Number of primes == 2 mod 3 dividing n.
• A005091 (program): Number of distinct primes = 3 mod 4 dividing n.
• A005092 (program): Sum of Fibonacci numbers 1,2,3,5,… that divide n.
• A005093 (program): Sum of squares of Fibonacci numbers 1,2,3,5,… that divide n.
• A005094 (program): Number of distinct primes of the form 4k+1 dividing n minus number of distinct primes of the form 4k+3 dividing n.
• A005095 (program): a(n) = n! + n.
• A005096 (program): a(n) = n! - n.
• A005097 (program): (Odd primes - 1)/2.
• A005098 (program): Numbers k such that 4k + 1 is prime.
• A005099 (program): (( Primes == -1 mod 4 ) + 1)/4.
• A005100 (program): Deficient numbers: numbers k such that sigma(k) < 2k.
• A005101 (program): Abundant numbers (sum of divisors of m exceeds 2m).
• A005117 (program): Squarefree numbers: numbers that are not divisible by a square greater than 1.
• A005118 (program): Number of simple allowable sequences on 1..n containing the permutation 12…n.
• A005122 (program): Numbers n such that 8n - 1 is prime.
• A005123 (program): Numbers n such that 8n + 1 is prime.
• A005124 (program): Numbers n such that 8n + 3 is prime.
• A005125 (program): Numbers n such that 8n - 3 is prime.
• A005126 (program): a(n) = 2^n + n + 1.
• A005131 (program): A generalized continued fraction for Euler’s number e.
• A005140 (program): Number of n-dimensional determinant 4 lattices.
• A005141 (program): Number of genera of forms with |determinant| = n.
• A005145 (program): n copies of n-th prime.
• A005152 (program): Rotation distance between binary trees on n nodes.
• A005153 (program): Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers.
• A005159 (program): a(n) = 3^n*Catalan(n).
• A005165 (program): Alternating factorials: n! - (n-1)! + (n-2)! - … 1!.
• A005168 (program): n-th derivative of x^x at 1, divided by n.
• A005171 (program): Characteristic function of nonprimes: 0 if n is prime, else 1.
• A005173 (program): Number of trees of subsets of an n-set.
• A005174 (program): Number of trees of subsets of an n-set.
• A005178 (program): Number of domino tilings of 4 X (n-1) board.
• A005181 (program): a(n) = ceiling(exp((n-1)/2)).
• A005182 (program): a(n) = floor(e^((n-1)/2)).
• A005183 (program): a(n) = n*2^(n-1) + 1.
• A005187 (program): a(n) = a(floor(n/2)) + n; also denominators in expansion of 1/sqrt(1-x) are 2^a(n); also 2n - number of 1’s in binary expansion of 2n.
• A005189 (program): Number of n-term 2-sided generalized Fibonacci sequences.
• A005190 (program): Central quadrinomial coefficients: largest coefficient of (1 + x + x^2 + x^3)^n.
• A005191 (program): Central pentanomial coefficients: largest coefficient of (1 + x + … + x^4)^n.
• A005193 (program): Balanced labeled graphs.
• A005203 (program): Fibonacci numbers (or rabbit sequence) converted to decimal.
• A005205 (program): Coding Fibonacci numbers.
• A005206 (program): Hofstadter G-sequence: a(0) = 0; a(n) = n - a(a(n-1)) for n > 0.
• A005207 (program): a(n) = (F(2*n-1) + F(n+1))/2 where F(n) is a Fibonacci number.
• A005209 (program): Multilevel sieve: at k-th step, accept k numbers, reject k, accept k, …
• A005210 (program): a(n) = |a(n-1) + 2a(n-2) - n|.
• A005212 (program): n! if n is odd otherwise 0 (from the Taylor series for sin x).
• A005213 (program): Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1).
• A005214 (program): Triangular numbers together with squares (excluding 0).
• A005225 (program): Number of permutations of length n with equal cycles.
• A005232 (program): Expansion of (1-x+x^2)/((1-x)^2*(1-x^2)*(1-x^4)).
• A005233 (program): A finite sequence associated with the Lie algebra A_5.
• A005237 (program): Numbers n such that n and n+1 have the same number of divisors.
• A005246 (program): a(n) = (1 + a(n-1)*a(n-2))/a(n-3), a(0) = a(1) = a(2) = 1.
• A005247 (program): a(n) = 3*a(n-2) - a(n-4), a(0)=2, a(1)=1, a(2)=3, a(3)=2. Alternates Lucas (A000032) and Fibonacci (A000045) sequences for even and odd n.
• A005248 (program): Bisection of Lucas numbers: a(n) = L(2*n) = A000032(2*n).
• A005249 (program): Determinant of inverse Hilbert matrix.
• A005251 (program): a(0) = 0, a(1) = a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
• A005252 (program): a(n) = Sum_{k=0..floor(n/4)} binomial(n-2k,2k).
• A005253 (program): Number of binary words not containing ..01110…
• A005254 (program): Number of weighted voting procedures.
• A005255 (program): Atkinson-Negro-Santoro sequence: a(n+1) = 2*a(n) - a(n-floor(n/2+1)).
• A005256 (program): Number of weighted voting procedures.
• A005257 (program): Number of weighted voting procedures.
• A005258 (program): Apéry numbers: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k).
• A005259 (program): Apery (Apéry) numbers: Sum_{k=0..n} (binomial(n,k)*binomial(n+k,k))^2.
• A005260 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^4.
• A005261 (program): a(n) = Sum_{k = 0..n} C(n,k)^5.
• A005262 (program): a(n) = floor((7*2^(n+1)-9*n-10)/3).
• A005267 (program): a(n) = -1 + a(0)a(1)…a(n-1) if n>0. a(0)=3.
• A005279 (program): Numbers having divisors d,e with d < e < 2*d.
• A005283 (program): Number of permutations of (1,…,n) having n-5 inversions (n>=5).
• A005284 (program): Number of permutations of (1,…,n) having n-6 inversions (n>=6).
• A005285 (program): Number of permutations of (1,…,n) having n-7 inversions (n>=7).
• A005286 (program): a(n) = (n + 3)*(n^2 + 6*n + 2)/6.
• A005287 (program): Number of permutations of [n] with four inversions.
• A005288 (program): a(n) = C(n,5) + C(n,4) - C(n,3) + 1, n >= 7.
• A005311 (program): Solution to Berlekamp’s switching game (or lightbulb game) on an n X n board.
• A005313 (program): Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.
• A005314 (program): For n = 0, 1, 2, a(n) = n; thereafter, a(n) = 2*a(n-1) - a(n-2) + a(n-3).
• A005317 (program): a(n) = (2^n + C(2*n,n))/2.
• A005319 (program): a(n) = 6*a(n-1) - a(n-2).
• A005320 (program): a(n) = 4*a(n-1) - a(n-2), with a(0) = 0, a(1) = 3.
• A005321 (program): Upper triangular n X n (0,1)-matrices with no zero rows or columns.
• A005322 (program): Column of Motzkin triangle.
• A005323 (program): Column of Motzkin triangle.
• A005324 (program): Column of Motzkin triangle A026300.
• A005325 (program): Column of Motzkin triangle.
• A005327 (program): Certain subgraphs of a directed graph (inverse binomial transform of A005321).
• A005328 (program): Certain subgraphs of a directed graph.
• A005329 (program): a(n) = Product_{i=1..n} (2^i - 1). Also called 2-factorial numbers.
• A005331 (program): Certain subgraphs of a directed graph (binomial transform of A005321).
• A005337 (program): Number of ways in which n identical balls can be distributed among 4 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.
• A005349 (program): Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.
• A005351 (program): Base -2 representation for n regarded as base 2, then evaluated.
• A005352 (program): Base -2 representation of -n reinterpreted as binary.
• A005353 (program): Number of 2 X 2 matrices with entries mod n and nonzero determinant.
• A005356 (program): Number of low discrepancy sequences in base 2.
• A005357 (program): Number of low discrepancy sequences in base 3.
• A005358 (program): Number of low discrepancy sequences in base 5.
• A005359 (program): a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x).
• A005361 (program): Product of exponents of prime factorization of n.
• A005367 (program): a(n) = 2*(2^n + 1)*(2^(n+1) - 1).
• A005369 (program): a(n) = 1 if n is of the form m(m+1), else 0.
• A005370 (program): a(n) = Fibonacci(Fibonacci(n+1) + 1).
• A005371 (program): a(n) = L(L(n)), where L(n) are Lucas numbers A000032.
• A005372 (program): a(n) = L(L(n+1)+1), where L(n) are Lucas numbers A000032.
• A005374 (program): Hofstadter H-sequence: a(n) = n - a(a(a(n-1))).
• A005375 (program): a(0) = 0; a(n) = n - a(a(a(a(n-1)))) for n > 0.
• A005377 (program): Number of low discrepancy sequences in base 4.
• A005378 (program): The female of a pair of recurrences.
• A005379 (program): The male of a pair of recurrences.
• A005380 (program): Expansion of 1 / Product_{k>=1} (1-x^k)^(k+1).
• A005381 (program): Numbers k such that k and k-1 are composite.
• A005382 (program): Primes p such that 2p-1 is also prime.
• A005383 (program): Primes p such that (p+1)/2 is prime.
• A005384 (program): Sophie Germain primes p: 2p+1 is also prime.
• A005385 (program): Safe primes p: (p-1)/2 is also prime.
• A005386 (program): Area of n-th triple of squares around a triangle.
• A005387 (program): Number of partitional matroids on n elements.
• A005388 (program): Number of degree-n permutations of order a power of 2.
• A005389 (program): Number of Hamiltonian circuits on 2n times 4 rectangle.
• A005403 (program): Number of protruded partitions of n with largest part at most 2.
• A005408 (program): The odd numbers: a(n) = 2*n + 1.
• A005409 (program): Number of polynomials of height n: a(1)=1, a(2)=1, a(3)=4, a(n) = 2*a(n-1) + a(n-2) + 2 for n >= 4.
• A005410 (program): a(n) = largest integer m such that every n-point interval order contains an m-point semiorder.
• A005416 (program): Vertex diagrams of order 2n.
• A005418 (program): Number of (n-1)-bead black-white reversible strings; also binary grids; also row sums of Losanitsch’s triangle A034851; also number of caterpillar graphs on n+2 vertices.
• A005425 (program): a(n) = 2*a(n-1) + (n-1)*a(n-2).
• A005427 (program): Josephus problem: numbers m such that, when m people are arranged on a circle and numbered 1 through m, the final survivor when we remove every 4th person is one of the first three people.
• A005428 (program): a(n) = ceiling((1 + sum of preceding terms) / 2) starting with a(0) = 1.
• A005429 (program): Apéry numbers: n^3*C(2n,n).
• A005430 (program): Apéry numbers: n*C(2*n,n).
• A005431 (program): Embeddings of n-bouquet in sphere.
• A005437 (program): Column of Kempner tableau.
• A005438 (program): Column of Kempner tableau.
• A005442 (program): a(n) = n!*Fibonacci(n+1).
• A005443 (program): a(n) = n! * Fibonacci(n).
• A005448 (program): Centered triangular numbers: a(n) = 3n(n-1)/2 + 1.
• A005449 (program): Second pentagonal numbers: a(n) = n*(3*n + 1)/2.
• A005450 (program): Numerator of (1 + Gamma(n))/n.
• A005453 (program): A finite sequence associated with the Lie algebra B_4.
• A005460 (program): a(n) = (3*n+4)*(n+3)!/24.
• A005461 (program): Number of simplices in barycentric subdivision of n-simplex.
• A005462 (program): Number of simplices in barycentric subdivision of n-simplex.
• A005463 (program): Number of simplices in barycentric subdivision of n-simplex.
• A005464 (program): Number of simplices in barycentric subdivision of n-simplex.
• A005465 (program): Number of n-dimensional hypotheses allowing for conditional independence.
• A005471 (program): Primes of the form m^2 + 3m + 9, where m can be positive or negative.
• A005473 (program): Primes of form k^2 + 4.
• A005475 (program): a(n) = n*(5*n+1)/2.
• A005476 (program): a(n) = n*(5*n - 1)/2.
• A005477 (program): a(n) = 2^(n-1)*(2^n - 1)*Product_{j=1..n-1} (2^j + 1).
• A005480 (program): Decimal expansion of cube root of 4.
• A005481 (program): Decimal expansion of cube root of 5.
• A005482 (program): Decimal expansion of cube root of 7.
• A005486 (program): Decimal expansion of cube root of 6.
• A005490 (program): Number of partitions of [n] where the first k elements are marked (0 <= k <= n-1) and at least k blocks contain their own index.
• A005491 (program): a(n) = n^3 + 3*n + 1.
• A005492 (program): From expansion of falling factorials.
• A005493 (program): 2-Bell numbers: a(n) = number of partitions of [n+1] with a distinguished block.
• A005494 (program): 3-Bell numbers: E.g.f.: exp(3*z + exp(z) - 1).
• A005498 (program): Triangulations of the disk G_{2,n}.
• A005508 (program): Number of unrooted triangulations with reflection symmetry of a disk with one internal node and n+3 nodes on the boundary.
• A005512 (program): Number of series-reduced labeled trees with n nodes.
• A005513 (program): Number of n-bead bracelets (turnover necklaces) of two colors with 6 red beads and n-6 black beads.
• A005517 (program): Smallest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling.
• A005521 (program): 1 + (sum of first n odd primes - n)/2.
• A005522 (program): a(n) = 1 + L(n) + F(2*n-1) with {L(n)}_{n>=0} the Lucas numbers (A000032) and F(2*n-1)_{n>=0} the bisected Fibonacci numbers (A001519).
• A005527 (program): Rational points on curves of genus n over GF(2).
• A005528 (program): Størmer numbers or arc-cotangent irreducible numbers: numbers k such that the largest prime factor of k^2 + 1 is >= 2*k.
• A005529 (program): Primitive prime factors of the sequence k^2 + 1 (A002522) in the order that they are found.
• A005531 (program): Decimal expansion of fifth root of 2.
• A005532 (program): Decimal expansion of fifth root of 3.
• A005533 (program): Decimal expansion of fifth root of 4.
• A005534 (program): Decimal expansion of fifth root of 5.
• A005536 (program): a(0) = 0; thereafter a(2n) = n - a(n) - a(n-1), a(2n+1) = n - 2a(n) + 1.
• A005554 (program): Sums of successive Motzkin numbers.
• A005557 (program): Number of walks on square lattice.
• A005558 (program): a(n) is the number of n-step walks on square lattice such that 0 <= y <= x at each step.
• A005559 (program): Number of walks on square lattice.
• A005560 (program): Number of walks on square lattice.
• A005561 (program): Number of walks on square lattice.
• A005562 (program): Number of walks on square lattice.
• A005563 (program): a(n) = n*(n+2) = (n+1)^2 - 1.
• A005564 (program): Number of n-step walks on square lattice in the first quadrant which finish at distance n-3 from the x-axis.
• A005565 (program): Number of walks on square lattice.
• A005566 (program): Number of walks of length n on square lattice, starting at origin, staying in first quadrant.
• A005567 (program): Number of walks on square lattice.
• A005568 (program): Product of two successive Catalan numbers C(n)*C(n+1).
• A005570 (program): Number of walks on cubic lattice.
• A005571 (program): Number of walks on cubic lattice.
• A005572 (program): Number of walks on cubic lattice starting and finishing on the xy plane and never going below it.
• A005573 (program): Number of walks on cubic lattice (starting from origin and not going below xy plane).
• A005574 (program): Numbers k such that k^2 + 1 is prime.
• A005578 (program): a(2*n) = 2*a(2*n-1), a(2*n+1) = 2*a(2*n)-1.
• A005581 (program): a(n) = (n-1)*n*(n+4)/6.
• A005582 (program): a(n) = n*(n+1)*(n+2)*(n+7)/24.
• A005583 (program): Coefficients of Chebyshev polynomials.
• A005584 (program): Coefficients of Chebyshev polynomials.
• A005585 (program): 5-dimensional pyramidal numbers: a(n) = n*(n+1)*(n+2)*(n+3)*(2n+3)/5!.
• A005586 (program): a(n) = n*(n+4)*(n+5)/6.
• A005587 (program): a(n) = n*(n+5)*(n+6)*(n+7)/24.
• A005590 (program): a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1) - a(n).
• A005592 (program): a(n) = F(2n+1) + F(2n-1) - 1.
• A005593 (program): a(n) = (F(2n+1) + F(2n-1) + F(n+3) - 2)/2, where F() = Fibonacci numbers A000045.
• A005594 (program): States of a dynamic storage system.
• A005595 (program): States of a dynamic storage system.
• A005598 (program): a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i).
• A005599 (program): Running sum of every third term in the {+1,-1}-version of Thue-Morse sequence A010060.
• A005601 (program): Decimal expansion of proton-to-electron mass ratio.
• A005605 (program): a(n) = a(n-1) + (-1)^(n-1) * a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
• A005609 (program): Number of Boolean functions realized by cascades of n gates.
• A005610 (program): Number of Boolean functions realized by cascades of n gates.
• A005612 (program): Number of Boolean functions of n variables that are variously called “unate cascades” or “1-decision list functions” or “read-once threshold functions”.
• A005614 (program): The binary complement of the infinite Fibonacci word A003849. Start with 1, apply 0->1, 1->10, iterate, take limit.
• A005618 (program): a(n) = 6*a(n-1) - 8.
• A005619 (program): Number of Boolean functions realized by n-input cascades.
• A005631 (program): Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details).
• A005647 (program): Salié numbers.
• A005649 (program): Expansion of e.g.f. (2 - e^x)^(-2).
• A005650 (program): Number of “magic squares” of order n (see comment line for exact definition).
• A005652 (program): Sum of 2 terms is never a Fibonacci number.
• A005653 (program): Sum of 2 terms is never a Fibonacci number.
• A005654 (program): Number of bracelets (turn over necklaces) with n red, 1 pink and n-1 blue beads; also reversible strings with n red and n-1 blue beads; also next-to-central column in Losanitsch’s triangle A034851.
• A005656 (program): Number of bracelets (turn over necklaces) with n red, 1 pink and n - 3 blue beads; also reversible strings with n red and n-3 blue beads.
• A005665 (program): Tower of Hanoi with 3 pegs and cyclic moves only (clockwise).
• A005666 (program): Tower of Hanoi with 3 pegs and cyclic moves only (counterclockwise).
• A005667 (program): Numerators of continued fraction convergents to sqrt(10).
• A005668 (program): Denominators of continued fraction convergents to sqrt(10).
• A005672 (program): a(n) = Fibonacci(n+1) - 2^floor(n/2).
• A005673 (program): F(n+1)-2^[ (n+1)/2 ] -2^[ n/2 ] +1.
• A005674 (program): a(n) = 2^(n-1) + 2^[ n/2 ] + 2^[ (n-1)/2 ] - F(n+3).
• A005676 (program): Sum C(n-k,4*k), k = 0..n.
• A005678 (program): A squarefree ternary sequence.
• A005679 (program): A squarefree (or Thue-Morse) ternary sequence: closed under a->abc, b->ac, c->b.
• A005680 (program): A squarefree ternary sequence.
• A005681 (program): A squarefree quaternary sequence.
• A005682 (program): Number of Twopins positions.
• A005683 (program): Numbers of Twopins positions.
• A005684 (program): Number of Twopins positions.
• A005685 (program): Number of Twopins positions.
• A005686 (program): Number of Twopins positions.
• A005689 (program): Number of Twopins positions.
• A005698 (program): Positions of remoteness 2 in Beans-Don’t-Talk.
• A005700 (program): a(n) = C(n)*C(n+2)-C(n+1)^2 where C() are the Catalan numbers A000108.
• A005701 (program): Number of exterior points formed by extending diagonals of n-gon in general position.
• A005704 (program): Number of partitions of 3n into powers of 3.
• A005705 (program): Number of partitions of 4*n into powers of 4.
• A005706 (program): Number of partitions of 5n into powers of 5.
• A005708 (program): a(n) = a(n-1) + a(n-6), with a(i) = 1 for i = 0..5.
• A005709 (program): a(n) = a(n-1) + a(n-7), with a(i) = 1 for i = 0..6.
• A005710 (program): a(n) = a(n-1) + a(n-8), with a(i) = 1 for i = 0..7.
• A005711 (program): a(n) = a(n-1) + a(n-9) for n >= 9; a(n) = 1 for n=0..7; a(8) = 2.
• A005712 (program): Coefficient of x^4 in expansion of (1+x+x^2)^n.
• A005713 (program): Define strings S(0)=0, S(1)=11, S(n) = S(n-1)S(n-2); iterate.
• A005714 (program): Coefficient of x^6 in expansion of (1+x+x^2)^n.
• A005715 (program): Coefficient of x^7 in expansion of (1+x+x^2)^n.
• A005716 (program): Coefficient of x^8 in expansion of (1+x+x^2)^n
• A005717 (program): Construct triangle in which n-th row is obtained by expanding (1 + x + x^2)^n and take the next-to-central column.
• A005718 (program): Quadrinomial coefficients: C(2+n,n) + C(3+n,n) + C(4+n,n).
• A005719 (program): Quadrinomial coefficients.
• A005720 (program): Quadrinomial coefficients.
• A005721 (program): Central quadrinomial coefficients.
• A005722 (program): a(n) = (prime(n) - 1)^2.
• A005723 (program): Quadrinomial coefficients.
• A005724 (program): Quadrinomial coefficients.
• A005725 (program): Quadrinomial coefficients.
• A005726 (program): Quadrinomial coefficients.
• A005727 (program): n-th derivative of x^x at x=1. Also called Lehmer-Comtet numbers.
• A005728 (program): Number of fractions in Farey series of order n.
• A005732 (program): a(n) = binomial(n+3,6) + binomial(n+1,5) + binomial(n,5).
• A005744 (program): G.f.: x*(1+x-x^2)/((1-x)^4*(1+x)).
• A005752 (program): a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2.
• A005758 (program): Number of partitions of n into parts of 12 kinds.
• A005766 (program): a(n) = cost of minimal multiplication-cost addition chain for n.
• A005767 (program): Solutions n to n^2 = a^2 + b^2 + c^2 (a,b,c > 0).
• A005773 (program): Number of directed animals of size n (or directed n-ominoes in standard position).
• A005774 (program): Number of directed animals of size n (k=1 column of A038622); number of (s(0), s(1), …, s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,…,n, where s(0) = 2; also sum of row n+1 of array T in A026323.
• A005775 (program): Number of compact-rooted directed animals of size n having 3 source points.
• A005779 (program): a(n) = largest integer such that every tournament on n nodes contains a consistent set of n arcs.
• A005783 (program): Number of 3-covers of an n-set.
• A005789 (program): 3-dimensional Catalan numbers.
• A005790 (program): 4-dimensional Catalan numbers.
• A005798 (program): Expansion of (theta_2(q)/theta_3(q))^4/16 in powers of q.
• A005802 (program): Number of permutations in S_n with longest increasing subsequence of length <= 3 (i.e., 1234-avoiding permutations); vexillary permutations (i.e., 2143-avoiding).
• A005803 (program): Second-order Eulerian numbers: a(n) = 2^n - 2*n.
• A005807 (program): Sum of adjacent Catalan numbers.
• A005809 (program): a(n) = binomial(3n,n).
• A005810 (program): a(n) = binomial(4n,n).
• A005811 (program): Number of runs in binary expansion of n (n>0); number of 1’s in Gray code for n.
• A005812 (program): Weight of balanced ternary representation of n.
• A005817 (program): a(n) = C(floor(n/2 + 1/2))*C(floor(n/2 + 1)) where C(i) = Catalan numbers A000108.
• A005818 (program): Numbers n that are primitive solutions to n^2 = a^2 + b^2 + c^2 (a,b,c > 0).
• A005819 (program): Number of words of length n in a certain language.
• A005821 (program): a(n) = [ tau*a(n-1) ] + a(n-2).
• A005823 (program): Numbers whose ternary expansion contains no 1’s.
• A005824 (program): a(n) = 5a(n-2) - 2a(n-4).
• A005825 (program): Numerators in a worst case of a Jacobi symbol algorithm.
• A005826 (program): Worst case of a Jacobi symbol algorithm.
• A005827 (program): Worst case of a Jacobi symbol algorithm.
• A005829 (program): a(n) = [ tau*a(n-1) ] + a(n-2).
• A005830 (program): a(n) = floor(tau*a(n-1)) + a(n-2) where tau is the golden ratio.
• A005831 (program): a(n+1) = a(n) * (a(n-1) + 1).
• A005833 (program): a(n) = [ tau*a(n-2) ] + a(n-1).
• A005834 (program): a(n) = floor( tau*a(n-2) ) + a(n-1) where tau is the golden ratio.
• A005836 (program): Numbers whose base 3 representation contains no 2.
• A005840 (program): Expansion of (1-x)*e^x/(2-e^x).
• A005843 (program): The nonnegative even numbers: a(n) = 2n.
• A005846 (program): Primes of the form n^2 + n + 41.
• A005855 (program): The coding-theoretic function A(n,10,7).
• A005856 (program): The coding-theoretic function A(n,10,8).
• A005857 (program): The coding-theoretic function A(n,12,7).
• A005860 (program): The coding-theoretic function A(n,12,10).
• A005861 (program): The coding-theoretic function A(n,14,9).
• A005862 (program): The coding-theoretic function A(n,14,10).
• A005867 (program): a(0) = 1; for n > 0, a(n) = (prime(n)-1)*a(n-1).
• A005868 (program): Molien series for 3-dimensional representation of Z2 X (double cover of A6), u.g.g.r. # 27 of Shephard and Todd.
• A005869 (program): Theta series of b.c.c. lattice with respect to short edge.
• A005872 (program): Theta series of hexagonal close-packing with respect to octahedral hole.
• A005875 (program): Theta series of simple cubic lattice; also number of ways of writing a nonnegative integer n as a sum of 3 squares (zero being allowed).
• A005876 (program): Theta series of cubic lattice with respect to edge.
• A005877 (program): Theta series of cubic lattice with respect to square.
• A005878 (program): Theta series of cubic lattice with respect to deep hole.
• A005879 (program): Theta series of D_4 lattice with respect to deep hole.
• A005880 (program): Theta series of D_4 lattice with respect to edge.
• A005881 (program): Theta series of planar hexagonal lattice (A2) with respect to edge.
• A005882 (program): Theta series of planar hexagonal lattice (A2) with respect to deep hole.
• A005883 (program): Theta series of square lattice with respect to deep hole.
• A005884 (program): Theta series of f.c.c. lattice with respect to edge.
• A005885 (program): Theta series of f.c.c. lattice with respect to triangle.
• A005886 (program): Theta series of f.c.c. lattice with respect to tetrahedral hole.
• A005887 (program): Theta series of f.c.c. lattice with respect to octahedral hole.
• A005891 (program): Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.
• A005892 (program): Truncated square numbers: 7*n^2 + 4*n + 1.
• A005893 (program): Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0).
• A005894 (program): Centered tetrahedral numbers.
• A005897 (program): a(n) = 6*n^2 + 2 for n > 0, a(0)=1.
• A005898 (program): Centered cube numbers: n^3 + (n+1)^3.
• A005899 (program): Number of points on surface of octahedron; also coordination sequence for cubic lattice: a(0) = 1; for n > 0, a(n) = 4n^2 + 2,
• A005900 (program): Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.
• A005901 (program): Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice.
• A005902 (program): Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.
• A005903 (program): Number of points on surface of dodecahedron: 30n^2 + 2 for n > 0.
• A005904 (program): Centered dodecahedral numbers.
• A005905 (program): Number of points on surface of truncated tetrahedron: 14n^2 + 2 for n>0, a(0)=1.
• A005906 (program): Truncated tetrahedral numbers: a(n) = (1/6)*(n+1)*(23*n^2 + 19*n + 6).
• A005907 (program): a(n) = [ tau*a(n-2) ] + a(n-1).
• A005908 (program): a(n) = floor( phi*a(n-1) ) + floor( phi*a(n-2) ), where phi is the golden ratio.
• A005909 (program): a(n) = [ tau*a(n-1) ] + [ tau*a(n-2) ].
• A005910 (program): Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6.
• A005911 (program): Number of points on surface of truncated cube: 46n^2 + 2.
• A005912 (program): Truncated cube numbers.
• A005913 (program): a(n) = [ tau*a(n-1) ] + [ tau*a(n-2) ].
• A005914 (program): Number of points on surface of hexagonal prism: 12*n^2 + 2 for n > 0 (coordination sequence for W(2)).
• A005915 (program): Hexagonal prism numbers: a(n) = (n + 1)*(3*n^2 + 3*n + 1).
• A005917 (program): Rhombic dodecahedral numbers: a(n) = n^4 - (n - 1)^4.
• A005918 (program): Number of points on surface of square pyramid: 3*n^2 + 2 (n>0).
• A005919 (program): Number of points on surface of tricapped prism: 7n^2 + 2 for n > 0, a(0)=1.
• A005920 (program): Tricapped prism numbers.
• A005921 (program): From solution to a difference equation.
• A005922 (program): a(1)=1; a(n) = n!*Fibonacci(n+2), n > 1.
• A005923 (program): From solution to a difference equation.
• A005928 (program): G.f.: s(1)^3/s(3), where s(k) = eta(q^k) and eta(q) is Dedekind’s function, cf. A010815.
• A005929 (program): Theta series of hexagonal net with respect to midpoint of edge.
• A005930 (program): Theta series of D_5 lattice.
• A005940 (program): The Doudna sequence: write n-1 in binary; power of prime(k) in a(n) is # of 1’s that are followed by k-1 0’s.
• A005941 (program): Inverse of the Doudna sequence A005940.
• A005942 (program): a(2n) = a(n) + a(n+1), a(2n+1) = 2a(n+1), if n >= 2.
• A005943 (program): Factor complexity (number of subwords of length n) of the Golay-Rudin-Shapiro binary word A020987.
• A005945 (program): Number of n-step mappings with 4 inputs.
• A005947 (program): Tumbling distance for n-input mappings with 2 steps.
• A005968 (program): Sum of cubes of first n Fibonacci numbers.
• A005969 (program): Sum of fourth powers of Fibonacci numbers.
• A005970 (program): Partial sums of squares of Lucas numbers.
• A005971 (program): Partial sums of cubes of Lucas numbers.
• A005972 (program): Partial sums of fourth powers of Lucas numbers.
• A005985 (program): Length of longest trail (i.e., path with all distinct edges) on the edges of an n-cube.
• A005989 (program): Values B(2,n)/4 of Gandhi polynomials defined by B(x,0)=x and B(x,n) = x^2 (B(x+1,n-1) - B(x,n-1)).
• A005990 (program): a(n) = (n-1)*(n+1)!/6.
• A005993 (program): Expansion of (1+x^2)/((1-x)^2*(1-x^2)^2).
• A005994 (program): Alkane (or paraffin) numbers l(7,n).
• A005995 (program): Alkane (or paraffin) numbers l(8,n).
• A005996 (program): G.f.: 2*(1-x^3)/((1-x)^5*(1+x)^2).
• A005997 (program): Number of paraffins.
• A005998 (program): Number of paraffins.
• A005999 (program): Number of paraffins.
• A006000 (program): a(n) = (n+1)*(n^2+n+2)/2; g.f.: (1 + 2*x^2) / (1 - x)^4.
• A006001 (program): Number of paraffins.
• A006002 (program): a(n) = n*(n+1)^2/2.
• A006003 (program): a(n) = n*(n^2 + 1)/2.
• A006004 (program): a(n) = C(n+2,3) + C(n,3) + C(n-1,3).
• A006005 (program): The odd prime numbers together with 1.
• A006007 (program): 4-dimensional analog of centered polygonal numbers: a(n) = n(n+1)*(n^2+n+4)/12.
• A006008 (program): Number of inequivalent ways to color vertices of a regular tetrahedron using <= n colors.
• A006009 (program): Number of paraffins.
• A006010 (program): Number of paraffins (see Losanitsch reference for precise definition).
• A006011 (program): a(n) = n^2*(n^2 - 1)/4.
• A006012 (program): a(0) = 1, a(1) = 2, a(n) = 4*a(n-1) - 2*a(n-2), n >= 2.
• A006013 (program): a(n) = binomial(3*n+1,n)/(n+1).
• A006015 (program): Nim product 2*n.
• A006022 (program): Sprague-Grundy (or Nim) values for the game of Maundy cake on an n X 1 sheet.
• A006040 (program): a(n) = Sum_{i=0..n} (n!/(n-i)!)^2.
• A006041 (program): a(n+1) = (n^2 - 1)*a(n) + n + 1.
• A006043 (program): A traffic light problem: expansion of 2/(1 - 3*x)^3.
• A006044 (program): a(n) = 4^(n-4)*(n-1)*(n-2)*(n-3).
• A006046 (program): Total number of odd entries in first n rows of Pascal’s triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). For n>0, a(n) = Sum_{i=0..n-1} 2^wt(i).
• A006047 (program): Number of entries in n-th row of Pascal’s triangle not divisible by 3.
• A006048 (program): Number of entries in first n rows of Pascal’s triangle not divisible by 3.
• A006049 (program): Numbers k such that k and k+1 have the same number of distinct prime divisors.
• A006051 (program): Square hex numbers.
• A006053 (program): a(n) = a(n-1) + 2*a(n-2) - a(n-3).
• A006054 (program): a(n) = 2*a(n-1) + a(n-2) - a(n-3), with a(0) = a(1) = 0, a(2) = 1.
• A006060 (program): Triangular star numbers.
• A006061 (program): Star numbers (A003154) that are squares.
• A006062 (program): Star-hex numbers.
• A006068 (program): a(n) is Gray-coded into n.
• A006071 (program): Maximal length of rook tour on an n X n board.
• A006072 (program): Numbers with mirror symmetry about middle.
• A006077 (program): (n+1)^2*a(n+1) = (9n^2+9n+3)*a(n) - 27*n^2*a(n-1), with a(0) = 1 and a(1) = 3.
• A006078 (program): Number of triangulated (n+2)-gons rooted at an exterior edge.
• A006079 (program): Number of asymmetric planted projective plane trees with n+1 nodes; bracelets (reversible necklaces) with n black beads and n-1 white beads.
• A006080 (program): Number of rooted projective plane trees with n nodes.
• A006081 (program): Number of line-rooted projective plane trees with n nodes.
• A006088 (program): a(n) = (2^n + 2) a(n-1) (kissing number of Barnes-Wall lattice in dimension 2^n).
• A006089 (program): Coefficients of elliptic function cn.
• A006090 (program): Expansion of bracket function.
• A006091 (program): a(n) = n^n - n + 1.
• A006093 (program): a(n) = prime(n) - 1.
• A006094 (program): Products of 2 successive primes.
• A006095 (program): Gaussian binomial coefficient [n,2] for q=2.
• A006096 (program): Gaussian binomial coefficient [ n,3 ] for q=2.
• A006097 (program): Gaussian binomial coefficient [ n,4 ] for q=2.
• A006098 (program): Gaussian binomial coefficient [ 2n,n ] for q=2.
• A006099 (program): Gaussian binomial coefficient [ n, n/2 ] for q=2.
• A006100 (program): Gaussian binomial coefficient [ n,2 ] for q=3.
• A006101 (program): Gaussian binomial coefficient [ n,3 ] for q=3.
• A006102 (program): Gaussian binomial coefficient [ n,4 ] for q=3.
• A006105 (program): Gaussian binomial coefficient [ n,2 ] for q=4.
• A006106 (program): Gaussian binomial coefficient [ n,3 ] for q = 4.
• A006107 (program): Gaussian binomial coefficient [ n,4 ] for q = 4.
• A006110 (program): Gaussian binomial coefficient [ n,5 ] for q = 2.
• A006111 (program): Gaussian binomial coefficient [ n,2 ] for q=5.
• A006112 (program): Gaussian binomial coefficient [ n,3 ] for q = 5.
• A006113 (program): Gaussian binomial coefficient [ n,4 ] for q = 5.
• A006116 (program): Sum of Gaussian binomial coefficients [n,k] for q=2 and k=0..n.
• A006117 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=3.
• A006118 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=4.
• A006119 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=5.
• A006120 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=6.
• A006121 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=7.
• A006122 (program): Sum of Gaussian binomial coefficients [ n,k ] for q=8.
• A006124 (program): a(n) = 3 + n/2 + 7*n^2/2.
• A006125 (program): a(n) = 2^(n*(n-1)/2).
• A006127 (program): a(n) = 2^n + n.
• A006129 (program): a(0), a(1), a(2), … satisfy Sum_{k=0..n} a(k)*binomial(n,k) = 2^binomial(n,2), for n >= 0.
• A006130 (program): a(n) = a(n-1) + 3*a(n-2) for n > 1, a(0) = a(1) = 1.
• A006131 (program): a(n) = a(n-1) + 4*a(n-2), a(0) = a(1) = 1.
• A006134 (program): a(n) = Sum_{k=0..n} binomial(2*k,k).
• A006137 (program): a(n) = 1 + n/2 + 9*n^2/2.
• A006138 (program): a(n) = a(n-1) + 3*a(n-2).
• A006139 (program): n*a(n) = 2*(2*n-1)*a(n-1) + 4*(n-1)*a(n-2) with a(0) = 1.
• A006149 (program): Number of Dyck paths.
• A006152 (program): Exponential generating function x*exp(x/(1-x)).
• A006153 (program): E.g.f.: 1/(1-x*exp(x)).
• A006154 (program): Number of labeled ordered partitions of an n-set into odd parts.
• A006155 (program): Expansion of e.g.f. 1/(2-x-e^x).
• A006157 (program): a(n+1) = (n-1)*a(n) + n*n!.
• A006165 (program): a(1) = a(2) = 1; thereafter a(2n+1) = a(n+1) + a(n), a(2n) = 2a(n).
• A006166 (program): a(0)=0, a(1)=a(2)=1; for n >= 1, a(3n+2) = 2a(n+1) + a(n), a(3n+1) = a(n+1) + 2a(n), a(3n) = 3a(n).
• A006171 (program): Number of factorization patterns of polynomials of degree n over integers.
• A006172 (program): a(n) = 1 + F(2*n+1) + (-1)^n*L(n).
• A006183 (program): a(n) = (n+1)*a(n-1) + (2-n)*a(n-2).
• A006184 (program): Number of cycles in the complement of a path.
• A006186 (program): Number of pair-coverings with largest block size 4.
• A006189 (program): Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with n rows and 3 columns.
• A006190 (program): a(n) = 3*a(n-1) + a(n-2), with a(0)=0, a(1)=1.
• A006191 (program): Number of paths on square lattice.
• A006192 (program): Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board.
• A006197 (program): Least number not dividing binomial(2n,n).
• A006198 (program): Number of partitions into pairs.
• A006199 (program): Bessel polynomial {y_n}’(-1).
• A006200 (program): Number of partitions into pairs.
• A006212 (program): Number of down-up permutations of n+3 starting with n+1.
• A006213 (program): Number of down-up permutations of n+4 starting with n+1.
• A006216 (program): Number of down-up permutations of n+4 starting with 4.
• A006217 (program): Number of down-up permutations of n+5 starting with 5.
• A006218 (program): a(n) = Sum_{k=1..n} floor(n/k); also Sum_{k=1..n} d(k), where d = number of divisors (A000005); also number of solutions to x*y = z with 1 <= x,y,z <= n.
• A006221 (program): From Apery continued fraction for zeta(3): zeta(3)=6/(5-1^6/(117-2^6/(535-3^6/(1463…))).
• A006222 (program): 11*n^2 + 11*n + 3.
• A006228 (program): Expansion of exp(arcsin(x)).
• A006230 (program): Bitriangular permutations.
• A006231 (program): a(n) = Sum_{k=2..n} n(n-1)…(n-k+1)/k.
• A006234 (program): a(n) = n*3^(n-4).
• A006235 (program): Complexity of doubled cycle (regarding case n = 2 as a multigraph).
• A006236 (program): n^(n-2)*(n+2)^(n-1).
• A006238 (program): Complexity of (or spanning trees in) a 3 X n grid.
• A006239 (program): Row 3 of array in A212801.
• A006244 (program): Hexagonal numbers (A000384) which are also centered hexagonal numbers (A003215).
• A006252 (program): Expansion of e.g.f. 1/(1 - log(1+x)).
• A006253 (program): Number of perfect matchings (or domino tilings) in C_4 X P_n.
• A006254 (program): Numbers k such that 2k-1 is prime.
• A006256 (program): a(n) = Sum_{k=0..n} binomial(3k,k)*binomial(3n-3k,n-k).
• A006257 (program): Josephus problem: a(2*n) = 2*a(n)-1, a(2*n+1) = 2*a(n)+1.
• A006261 (program): a(n) = Sum_{k=0..5} C(n,k).
• A006264 (program): Diagonal length function.
• A006277 (program): a(n) = (a(n-1) + 1)*a(n-2).
• A006278 (program): a(n) is the product of the first n primes congruent to 1 (mod 4).
• A006279 (program): Denominators of convergents to Cahen’s constant: a(n+2) = a(n)^2*a(n+1) + a(n).
• A006280 (program): Partial quotients in continued fraction expansion of Cahen’s constant.
• A006282 (program): Sorting numbers: number of comparisons in Batcher’s parallel sort.
• A006287 (program): Sum of squares of digits of ternary representation of n.
• A006288 (program): Loxton-van der Poorten sequence: base-4 representation contains only -1, 0, +1.
• A006298 (program): Number of genus 2 rooted maps with 1 face with n vertices.
• A006308 (program): Coefficients of period polynomials.
• A006318 (program): Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).
• A006319 (program): Royal paths in a lattice (convolution of A006318).
• A006320 (program): Royal paths in a lattice.
• A006321 (program): Royal paths in a lattice.
• A006322 (program): 4-dimensional analog of centered polygonal numbers.
• A006323 (program): 4-dimensional analog of centered polygonal numbers.
• A006324 (program): a(n) = n*(n + 1)*(2*n^2 + 2*n - 1)/6.
• A006325 (program): 4-dimensional analog of centered polygonal numbers.
• A006326 (program): Total preorders.
• A006327 (program): a(n) = Fibonacci(n) - 3. Number of total preorders.
• A006328 (program): Total preorders.
• A006331 (program): a(n) = n*(n+1)*(2*n+1)/3.
• A006332 (program): From the enumeration of corners.
• A006333 (program): From the enumeration of corners.
• A006334 (program): From the enumeration of corners.
• A006335 (program): a(n) = 4^n*(3*n)!/((n+1)!*(2*n+1)!).
• A006337 (program): An “eta-sequence”: a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).
• A006338 (program): An “eta-sequence”: floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2).
• A006340 (program): An “eta-sequence”: [ (n+1)*tau + 1/2 ] - [ n*tau + 1/2 ], tau = (1 + sqrt(5))/2.
• A006342 (program): Coloring a circuit with 4 colors.
• A006347 (program): a(n) = (n+1) a(n-1) + (-1)^n.
• A006348 (program): a(n) = (n+2)*a(n-1) + (-1)^n.
• A006352 (program): Coefficients in expansion of Eisenstein series E_2 (also called E_1 or G_2).
• A006353 (program): Expansion of (phi(-q^3) * psi(q))^3 / (phi(-q) * psi(q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.
• A006355 (program): Number of binary vectors of length n containing no singletons.
• A006356 (program): a(n) = 2*a(n-1) + a(n-2) - a(n-3) for n >= 3, starting with a(0) = 1, a(1) = 3, and a(2) = 6.
• A006357 (program): Number of distributive lattices; also number of paths with n turns when light is reflected from 4 glass plates.
• A006358 (program): Number of distributive lattices; also number of paths with n turns when light is reflected from 5 glass plates.
• A006359 (program): Number of distributive lattices; also number of paths with n turns when light is reflected from 6 glass plates.
• A006364 (program): Numbers n with an even number of 1’s in binary, ignoring last bit.
• A006367 (program): Number of binary vectors of length n+1 beginning with 0 and containing just 1 singleton.
• A006368 (program): The “amusical permutation” of the nonnegative numbers: a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1.
• A006369 (program): a(n) = 2*n/3 for n divisible by 3, otherwise a(n) = round(4*n/3). Or, equivalently, a(3*n-2) = 4*n-3, a(3*n-1) = 4*n-1, a(3*n) = 2*n.
• A006370 (program): The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd.
• A006380 (program): Number of equivalence classes of 4 X n binary matrices when one can permute rows, permute columns and complement columns.
• A006411 (program): Number of nonseparable tree-rooted planar maps with n + 2 edges and 3 vertices.
• A006414 (program): Number of nonseparable toroidal tree-rooted maps with n + 2 edges and n + 1 vertices.
• A006416 (program): Number of loopless rooted planar maps with 3 faces and n vertices and no isthmuses. Also a(n)=T(4,n-3), array T as in A049600.
• A006419 (program): a(n) = 2^(2*n+1) - C(2*n+3,n+1) + C(2*n+1,n).
• A006428 (program): Number of loopless tree-rooted planar maps with 3 vertices and n faces and no isthmuses.
• A006438 (program): Expansion of e.g.f. 1/sqrt(1-8x+x^2).
• A006442 (program): Expansion of 1/sqrt(1 - 10*x + x^2).
• A006446 (program): Numbers k such that floor(sqrt(k)) divides k.
• A006449 (program): Row sums of Fibonacci-Pascal triangle in A045995.
• A006450 (program): Prime-indexed primes: primes with prime subscripts.
• A006451 (program): Numbers k such that k*(k+1)/2 + 1 is a square.
• A006452 (program): a(n) = 6*a(n-2) - a(n-4).
• A006453 (program): Expansion of 1/sqrt(1 - 12x + x^2).
• A006454 (program): Solution to a Diophantine equation: each term is a triangular number and each term + 1 is a square.
• A006456 (program): Number of compositions (ordered partitions) of n into squares.
• A006457 (program): Number of elements in Z[ i ] whose ‘smallest algorithm’ is <= n.
• A006460 (program): Image of n after 3k iterates of ‘3x+1’ map (k large).
• A006463 (program): Convolve natural numbers with characteristic function of triangular numbers.
• A006464 (program): Continued fraction for Sum_{n>=0} 1/4^(2^n).
• A006468 (program): Number of rooted planar maps with 4 faces and n vertices and no isthmuses.
• A006470 (program): Number of tree-rooted planar maps with 3 faces and n vertices and no isthmuses.
• A006472 (program): a(n) = n!*(n-1)!/2^(n-1).
• A006474 (program): Related to Ramsey numbers.
• A006477 (program): Number of partitions of n with at least 1 odd and 1 even part.
• A006478 (program): a(n) = a(n-1) + a(n-2) + F(n) - 1, a(0) = a(1) = 0, where F() = Fibonacci numbers A000045.
• A006479 (program): From variance of Fibonacci search.
• A006480 (program): De Bruijn’s S(3,n): (3n)!/(n!)^3.
• A006481 (program): Euler characteristics of polytopes.
• A006483 (program): a(n) = Fibonacci(n)*2^n + 1.
• A006484 (program): a(n) = n*(n + 1)*(n^2 - 3*n + 5)/6.
• A006490 (program): a(1) = 1, a(2) = 0; for n > 2, a(n) = n*Fibonacci(n-2) (with the convention Fibonacci(0)=0, Fibonacci(1)=1).
• A006491 (program): Generalized Lucas numbers.
• A006492 (program): Generalized Lucas numbers.
• A006493 (program): Generalized Lucas numbers.
• A006495 (program): Real part of (1 + 2*i)^n, where i is sqrt(-1).
• A006496 (program): Imaginary part of (1+2i)^n.
• A006497 (program): a(n) = 3*a(n-1) + a(n-2) with a(0) = 2, a(1) = 3.
• A006498 (program): a(n) = a(n-1) + a(n-3) + a(n-4), a(0) = a(1) = a(2) = 1, a(3) = 2.
• A006499 (program): Number of restricted circular combinations.
• A006500 (program): Restricted combinations.
• A006501 (program): Expansion of (1+x^2) / ( (1-x)^2 * (1-x^3)^2 ).
• A006503 (program): a(n) = n*(n+1)*(n+8)/6.
• A006504 (program): Coefficient of x^4 in (1-x-x^2)^(-n).
• A006505 (program): Number of partitions of an n-set into boxes of size >2.
• A006507 (program): a(n+1) = a(n) + sum of digits of a(n), with a(1)=7.
• A006512 (program): Greater of twin primes.
• A006513 (program): Limit of the image of n after 2k iterates of `(3x+1)/2’ map as k grows.
• A006516 (program): a(n) = 2^(n-1)*(2^n - 1), n >= 0.
• A006519 (program): Highest power of 2 dividing n.
• A006520 (program): Partial sums of A006519.
• A006522 (program): 4-dimensional analog of centered polygonal numbers. Also number of regions created by sides and diagonals of a convex n-gon in general position.
• A006527 (program): a(n) = (n^3 + 2*n)/3.
• A006528 (program): a(n) = (n^4 + n^2 + 2*n)/4.
• A006530 (program): Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1.
• A006532 (program): Numbers whose sum of divisors is a square.
• A006542 (program): a(n) = binomial(n,3)*binomial(n-1,3)/4.
• A006547 (program): Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).
• A006548 (program): (2*n)!-Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n).
• A006551 (program): Maximal Eulerian numbers.
• A006564 (program): Icosahedral numbers: a(n) = n*(5*n^2 - 5*n + 2)/2.
• A006565 (program): Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations.
• A006566 (program): Dodecahedral numbers: a(n) = n*(3*n - 1)*(3*n - 2)/2.
• A006577 (program): Number of halving and tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
• A006578 (program): Triangular numbers plus quarter squares: n*(n+1)/2 + floor(n^2/4) (i.e., A000217(n) + A002620(n)).
• A006579 (program): a(n) = Sum_{k=1..n-1} gcd(n,k).
• A006580 (program): a(n) = Sum_{k=1..n-1} lcm(k,n-k).
• A006581 (program): a(n) = Sum_{k=1..n-1} (k AND n-k).
• A006582 (program): a(n) = Sum_{k=1..n-1} k XOR n-k.
• A006583 (program): a(n) = Sum_{k=1..n-1} (k OR n-k).
• A006584 (program): If n mod 2 = 0 then n*(n^2-4)/12 else n*(n^2-1)/12.
• A006586 (program): a(n) = Sum_{k=1..n} floor((2n-1)/(2k+1)).
• A006587 (program): a(n) = 3*2^(2*n)*(3*n)!/((2*n)!*n!).
• A006588 (program): a(n) = 4^n*(3*n)!/((2*n)!*n!).
• A006589 (program): a(n) = (n+3)*2^n - 1.
• A006590 (program): a(n) = Sum_{k=1..n} ceiling(n/k).
• A006591 (program): a(n) = Sum_{k=1..n} nearest integer to n/k (if n/k is midway between two numbers take the smaller).
• A006592 (program): a(n) = 10*n^3 - 6*n^2.
• A006594 (program): A Beatty sequence: [ n(1 + 1/e) ].
• A006595 (program): a(n) = (n+2)!/4 + n!/2.
• A006597 (program): a(n) = n^2*(5*n-3)/2.
• A006603 (program): Generalized Fibonacci numbers.
• A006604 (program): Generalized Fibonacci numbers.
• A006605 (program): Number of modes of connections of 2n points.
• A006617 (program): Zarankiewicz’s problem.
• A006620 (program): Zarankiewicz’s problem.
• A006621 (program): Zarankiewicz’s problem k_3(n,n+1).
• A006629 (program): Self-convolution 4th power of A001764, which enumerates ternary trees.
• A006630 (program): From generalized Catalan numbers.
• A006631 (program): From generalized Catalan numbers.
• A006632 (program): a(n) = 3*binomial(4*n-1,n-1)/(4*n-1).
• A006633 (program): From generalized Catalan numbers.
• A006634 (program): From generalized Catalan numbers.
• A006635 (program): From generalized Catalan numbers.
• A006636 (program): From generalized Catalan numbers.
• A006637 (program): From generalized Catalan numbers.
• A006645 (program): Self-convolution of Pell numbers (A000129).
• A006646 (program): Exponential self-convolution of Pell numbers.
• A006659 (program): Number of closed meander systems of order n+1 with n components.
• A006666 (program): Number of halving steps to reach 1 in ‘3x+1’ problem, or -1 if this never happens.
• A006667 (program): Number of tripling steps to reach 1 from n in ‘3x+1’ problem, or -1 if 1 is never reached.
• A006668 (program): Exponential self-convolution of Pell numbers (divided by 2).
• A006671 (program): Edge-distinguishing chromatic number of cycle with n nodes.
• A006672 (program): Ramsey numbers.
• A006675 (program): Number of paths through an array.
• A006677 (program): Number of planted binary phylogenetic trees with n labels.
• A006681 (program): Number of binary phylogenetic trees with n labels.
• A006684 (program): Convolve Fibonacci and Pell numbers.
• A006695 (program): a(2n)=2*a(2n-2)^2-1, a(2n+1)=2a(2n)-1, a(0)=2.
• A006697 (program): Number of subwords of length n in infinite word generated by a -> aab, b -> b.
• A006720 (program): Somos-4 sequence: a(0)=a(1)=a(2)=a(3)=1; for n >= 4, a(n) = (a(n-1) * a(n-3) + a(n-2)^2) / a(n-4).
• A006721 (program): Somos-5 sequence: a(n) = (a(n-1) * a(n-4) + a(n-2) * a(n-3)) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
• A006722 (program): Somos-6 sequence: a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = … = a(5) = 1.
• A006723 (program): Somos-7 sequence: a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-5) + a(n-3) * a(n-4)) / a(n-7), a(0) = … = a(6) = 1.
• A006769 (program): Elliptic divisibility sequence associated with elliptic curve “37a1”: y^2 + y = x^3 - x and multiples of the point (0,0).
• A006788 (program): a(n) = floor(2^(n-1)/n).
• A006833 (program): Decimal expansion of neutron-to-electron mass ratio.
• A006834 (program): Decimal expansion of neutron-to-proton mass ratio.
• A006847 (program): Number of extreme points of the set of n X n symmetric doubly-stochastic matrices.
• A006857 (program): a(n) = binomial(n+5,5) * binomial(n+5,4)/(n+5).
• A006858 (program): Expansion of x*(1 + x)*(1 + 6*x + x^2)/(1 - x)^7.
• A006859 (program): From paths in the plane.
• A006862 (program): Euclid numbers: 1 + product of the first n primes.
• A006863 (program): Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.
• A006864 (program): Number of Hamiltonian cycles in P_4 X P_n.
• A006865 (program): Number of Hamiltonian cycles in P_5 X P_{2n}: a(n) = 11a(n-1)+2a(n-3).
• A006875 (program): Non-seed mu-atoms of period n in Mandelbrot set.
• A006881 (program): Squarefree semiprimes: Numbers that are the product of two distinct primes.
• A006882 (program): Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.
• A006888 (program): a(n) = a(n-1) + a(n-2)*a(n-3) for n > 2 with a(0) = a(1) = a(2) = 1.
• A006892 (program): Representation as a sum of squares requires n squares with greedy algorithm.
• A006893 (program): Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
• A006894 (program): Number of planted 3-trees of height < n.
• A006896 (program): a(n) is the number of hierarchical linear models on n labeled factors allowing 2-way interactions (but no higher order interactions); or the number of simple labeled graphs with nodes chosen from an n-set.
• A006898 (program): a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).
• A006899 (program): Numbers of the form 2^i or 3^j.
• A006902 (program): a(n) = (2n)! * Sum_{k=0..n} (-1)^k * binomial(n,k) / (n+k)!.
• A006904 (program): a(n) = a(n-1) + 2*a(n-2) + (-1)^n.
• A006906 (program): a(n) is the sum of products of terms in all partitions of n.
• A006918 (program): a(n) = binomial(n+3, 3)/4, n odd; n(n+2)(n+4)/24, n even.
• A006921 (program): Diagonals of Pascal’s triangle mod 2 interpreted as binary numbers.
• A006922 (program): Expansion of 1/eta(q)^24; Fourier coefficients of T_{14}.
• A006928 (program): a(n) = length of (n+1)st run, with initial terms 1, 2.
• A006932 (program): Number of permutations of [n] with at least one strong fixed point (a permutation p of {1,2,…,n} is said to have j as a strong fixed point if p(k) < j for k < j and p(k) > j for k > j).
• A006939 (program): Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1).
• A006940 (program): Rows of Pascal’s triangle mod 3.
• A006943 (program): Rows of Sierpiński’s triangle (Pascal’s triangle mod 2).
• A006946 (program): Independence number of De Bruijn graph of order n on two symbols.
• A006949 (program): A well-behaved cousin of the Hofstadter sequence: a(n) = a(n - 1 - a(n-1)) + a(n - 2 - a(n-2)) for n > 2 with a(0) = a(1) = a(2) = 1.
• A006950 (program): G.f.: Product_{k>=1} (1 + x^(2*k - 1)) / (1 - x^(2*k)).
• A006953 (program): a(n) = denominator of Bernoulli(2n)/(2n).
• A006954 (program): Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, …
• A006955 (program): Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
• A006956 (program): Denominator of (2n+1)(2n+2) B_{2n}, where B_n are the Bernoulli numbers. Also denominators of the asymptotic expansion of the polygamma function psi’’‘(z).
• A006960 (program): Reverse and Add! sequence starting with 196.
• A006963 (program): Number of planar embedded labeled trees with n nodes: (2n-3)!/(n-1)! for n >= 2, a(1) = 1.
• A006974 (program): Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0.
• A006975 (program): Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+10, n), n >= 0.
• A006976 (program): Coefficients of Chebyshev T polynomials: a(n) = A053120(n+12, n), n >= 0.
• A006977 (program): Cellular automaton with Rule 230: 000, 001, 010, 011, …, 111 -> 0,1,1,0,0,1,1,1.
• A006978 (program): Successive states of the Rule 110 cellular automaton defined by 000, 001, 010, 011, …, 111 -> 0,1,1,1,0,1,1,0 when started with a single ON cell.
• A006995 (program): Binary palindromes: numbers whose binary expansion is palindromic.
• A006996 (program): C(2n,n) mod 3.
• A006998 (program): Partitioning integers to avoid arithmetic progressions of length 3.
• A006999 (program): Partitioning integers to avoid arithmetic progressions of length 3.
• A007000 (program): Number of partitions of n into Fibonacci parts (with 2 types of 1).
• A007001 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 123, 3 -> 1234, etc.
• A007004 (program): a(n) = (3*n)! / ((n+1)*(n!)^3).
• A007007 (program): Valence of graph of maximal intersecting families of sets.
• A007008 (program): Chvatal conjecture for radius of graph of maximal intersecting sets.
• A007009 (program): Number of 3-voter voting schemes with n linearly ranked choices.
• A007019 (program): a(n) = (2n+1)! / 2^n.
• A007039 (program): Number of cyclic binary n-bit strings with no alternating substring of length > 2.
• A007040 (program): Number of (marked) cyclic n-bit binary strings containing no runs of length > 2.
• A007042 (program): Left diagonal of partition triangle A047812.
• A007044 (program): Left diagonal of partition triangle A047812.
• A007047 (program): Number of chains in power set of n-set.
• A007051 (program): a(n) = (3^n + 1)/2.
• A007052 (program): Number of order-consecutive partitions of n.
• A007054 (program): Super ballot numbers: 6(2n)!/(n!(n+2)!).
• A007060 (program): Number of ways n couples can sit in a row without any spouses next to each other.
• A007062 (program): Let P(n) of a sequence s(1),s(2),s(3),… be obtained by leaving s(1),…,s(n) fixed and reversing every n consecutive terms thereafter; apply P(2) to 1,2,3,… to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is A007062.
• A007064 (program): Numbers not of form “nearest integer to n*tau”, tau = (1+sqrt(5))/2.
• A007066 (program): a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2.
• A007067 (program): Nearest integer to n*tau.
• A007068 (program): a(n) = a(n-1) + (3+(-1)^n)*a(n-2)/2.
• A007069 (program): First column of spectral array W(sqrt 2).
• A007070 (program): a(n) = 4*a(n-1) - 2*a(n-2) with a(0) = 1, a(1) = 4.
• A007071 (program): First row of 2-shuffle of spectral array W( sqrt 2 ).
• A007073 (program): First column of array associated with lexicographically justified array.
• A007088 (program): The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.
• A007089 (program): Numbers in base 3.
• A007090 (program): Numbers in base 4.
• A007091 (program): Numbers in base 5.
• A007092 (program): Numbers in base 6.
• A007093 (program): Numbers in base 7.
• A007094 (program): Numbers in base 8.
• A007095 (program): Numbers in base 9.
• A007106 (program): Number of labeled odd degree trees with 2n nodes.
• A007123 (program): Number of connected unit interval graphs with n nodes; also number of bracelets (turnover necklaces) with n black beads and n-1 white beads.
• A007147 (program): Number of self-dual 2-colored necklaces with 2n beads.
• A007148 (program): Number of self-complementary 2-colored bracelets (turnover necklaces) with 2n beads.
• A007160 (program): Number of diagonal dissections of a convex (n+6)-gon into n regions.
• A007165 (program): Number of P-graphs with 2n edges.
• A007179 (program): Dual pairs of integrals arising from reflection coefficients.
• A007185 (program): Automorphic numbers ending in digit 5: a(n) = 5^(2^n) mod 10^n.
• A007191 (program): McKay-Thompson series of class 2B for the Monster group with a(0) = -24.
• A007202 (program): Crystal ball sequence for hexagonal close-packing.
• A007204 (program): Crystal ball sequence for D_4 lattice.
• A007223 (program): Number of distinct perforation patterns for deriving (v,b) = (n+2,n) punctured convolutional codes from (2,1).
• A007224 (program): Number of distinct perforation patterns for deriving (v,b) = (n+3,n) punctured convolutional codes from (2,1).
• A007226 (program): a(n) = 2*det(M(n; -1))/det(M(n; 0)), where M(n; m) is the n X n matrix with (i,j)-th element equal to 1/binomial(n + i + j + m, n).
• A007228 (program): a(n) = 3*binomial(4*n,n)/(n+1).
• A007238 (program): Length of longest chain of subgroups in S_n.
• A007244 (program): McKay-Thompson series of class 3B for the Monster group.
• A007246 (program): McKay-Thompson series of class 2B for the Monster group.
• A007248 (program): McKay-Thompson series of class 4C for the Monster group.
• A007249 (program): McKay-Thompson series of class 4D for the Monster group.
• A007252 (program): McKay-Thompson series of class 5B for the Monster group with a(0) = 0.
• A007255 (program): McKay-Thompson series of class 6B for Monster.
• A007257 (program): McKay-Thompson series of class 6D for Monster.
• A007258 (program): McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
• A007259 (program): Expansion of Product_{m>=1} (1 + q^m)^(-8).
• A007262 (program): McKay-Thompson series of class 6c for Monster.
• A007272 (program): Super ballot numbers: 60(2n)!/(n!(n+3)!).
• A007281 (program): Number of `(n,2)’-sequences of length 2n.
• A007283 (program): a(n) = 3*2^n.
• A007286 (program): E.g.f.: (sin x + cos 2x) / cos 3x.
• A007290 (program): a(n) = 2*binomial(n,3).
• A007291 (program): Series expansion for rectilinear polymers on square lattice.
• A007293 (program): Dimension of space of weight systems of chord diagrams.
• A007294 (program): Number of partitions of n into nonzero triangular numbers.
• A007297 (program): Number of connected graphs on n labeled nodes on a circle with straight-line edges that don’t cross.
• A007298 (program): Sums of consecutive Fibonacci numbers.
• A007302 (program): Optimal cost function between two processors at distance n.
• A007304 (program): Sphenic numbers: products of 3 distinct primes.
• A007305 (program): Numerators of Farey (or Stern-Brocot) tree fractions.
• A007306 (program): Denominators of Farey tree fractions (i.e., the Stern-Brocot subtree in the range [0,1]).
• A007307 (program): a(n) = a(n-2) + a(n-3).
• A007309 (program): a(n)=a(n-2)+a(n-3).
• A007310 (program): Numbers congruent to 1 or 5 mod 6.
• A007317 (program): Binomial transform of Catalan numbers.
• A007318 (program): Pascal’s triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n.
• A007325 (program): G.f.: Product_{k>0} (1-x^(5k-1))*(1-x^(5k-4))/((1-x^(5k-2))*(1-x^(5k-3))).
• A007331 (program): Fourier coefficients of E_{infinity,4}.
• A007334 (program): Number of spanning trees in the graph K_{n}/e, which results from contracting an edge e in the complete graph K_{n} on n vertices (for n>=2).
• A007339 (program): a(n) = n! - n^3.
• A007345 (program): Number of Havender tableaux of height 2 with n columns.
• A007369 (program): Numbers n such that sigma(x) = n has no solution.
• A007378 (program): a(n), for n >= 2, is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n.
• A007380 (program): Number of 5th-order maximal independent sets in path graph.
• A007381 (program): 7th-order maximal independent sets in path graph.
• A007382 (program): Number of strict (-1)st-order maximal independent sets in path graph.
• A007383 (program): Number of strict first-order maximal independent sets in path graph.
• A007384 (program): Number of strict 3rd-order maximal independent sets in path graph.
• A007385 (program): Number of strict 5th-order maximal independent sets in path graph.
• A007386 (program): Number of strict 7th-order maximal independent sets in path graph.
• A007387 (program): Number of 3rd-order maximal independent sets in cycle graph.
• A007390 (program): Number of strict (-1)st-order maximal independent sets in cycle graph.
• A007391 (program): Number of strict first-order maximal independent sets in cycle graph.
• A007395 (program): Constant sequence: the all 2’s sequence.
• A007396 (program): Add 2, then reverse digits!.
• A007397 (program): Add 5, then reverse digits!.
• A007398 (program): Add 7, then reverse digits.
• A007399 (program): Add 8, then reverse digits!.
• A007400 (program): Continued fraction for Sum_{n>=0} 1/2^(2^n) = 0.8164215090218931…
• A007401 (program): Add n-1 to n-th term of ‘n appears n times’ sequence (A002024).
• A007403 (program): a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^3 = (n+2)*2^(3*n-1) - 3*2^(n-2)*n*binomial(2*n,n).
• A007404 (program): Decimal expansion of Sum_{n>=0} 1/2^(2^n).
• A007405 (program): Dowling numbers: e.g.f.: exp(x + (exp(b*x) - 1)/b) with b=2.
• A007406 (program): Wolstenholme numbers: numerator of Sum_{k=1..n} 1/k^2.
• A007407 (program): a(n) = denominator of Sum_{k=1..n} 1/k^2.
• A007408 (program): Wolstenholme numbers: numerator of Sum_{k=1..n} 1/k^3.
• A007409 (program): Denominators of Sum_{k=1..n} 1/k^3.
• A007410 (program): Numerator of Sum_{k=1..4} k^(-4).
• A007412 (program): The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3)).
• A007413 (program): A squarefree (or Thue-Morse) ternary sequence: closed under 1->123, 2->13, 3->2. Start with 1.
• A007415 (program): Expand sin x / exp x = x-x^2+x^3/3-x^5/30+… and invert nonzero coefficients.
• A007417 (program): If k appears, 3k does not.
• A007420 (program): Berstel sequence: a(n+1) = 2*a(n) - 4*a(n-1) + 4*a(n-2).
• A007421 (program): Liouville’s function: parity of number of primes dividing n (with multiplicity).
• A007422 (program): Multiplicatively perfect numbers j: product of divisors of j is j^2.
• A007423 (program): a(n) = mu(n) + 1, where mu is the Moebius function.
• A007424 (program): a(n) = 1 if n is squarefree, otherwise 2.
• A007425 (program): d_3(n), or tau_3(n), the number of ordered factorizations of n as n = r s t.
• A007426 (program): d_4(n), or tau_4(n), the number of ordered factorizations of n as n = rstu.
• A007427 (program): Moebius transform applied twice to sequence 1,0,0,0,….
• A007428 (program): Moebius transform applied thrice to sequence 1,0,0,0,….
• A007429 (program): Inverse Moebius transform applied twice to natural numbers.
• A007430 (program): Inverse Moebius transform applied thrice to natural numbers.
• A007431 (program): a(n) = Sum_{d|n} phi(d)*mu(n/d).
• A007432 (program): Moebius transform applied thrice to natural numbers.
• A007433 (program): Inverse Moebius transform applied twice to squares.
• A007434 (program): Jordan function J_2(n) (a generalization of phi(n)).
• A007435 (program): Inverse Moebius transform of Fibonacci numbers 1,1,2,3,5,8,…
• A007437 (program): Inverse Moebius transform of triangular numbers.
• A007438 (program): Moebius transform of triangular numbers.
• A007439 (program): Number of planted trees: all sub-rooted trees from any node are identical; non-root, non-leaf nodes an even distance from the root are of degree 2.
• A007440 (program): Reversion of g.f. for Fibonacci numbers 1, 1, 2, 3, 5, ….
• A007442 (program): Inverse binomial transform of primes.
• A007443 (program): Binomial transform of primes.
• A007444 (program): Moebius transform of primes.
• A007445 (program): Inverse Moebius transform of primes.
• A007450 (program): Decimal expansion of 1/17.
• A007452 (program): Expand cos x / exp x and invert nonzero coefficients.
• A007455 (program): Number of subsequences of [ 1,…,n ] in which each odd number has an even neighbor.
• A007456 (program): Number of days required to spread gossip to n people.
• A007457 (program): Number of (j,k): j+k=n, (j,n)=(k,n)=1, j,k squarefree.
• A007465 (program): Exponential-convolution of triangular numbers with themselves.
• A007466 (program): Exponential-convolution of natural numbers with themselves.
• A007468 (program): Sum of next n primes.
• A007472 (program): Shifts 2 places left when binomial transform is applied twice.
• A007473 (program): Dimension of space of Vassiliev knot invariants of order n.
• A007476 (program): Shifts 2 places left under binomial transform.
• A007477 (program): Shifts 2 places left when convolved with itself.
• A007478 (program): Dimension of primitive Vassiliev knot invariants of order n.
• A007480 (program): a(n) = denominator of sum_{k=1..n} k^(-4).
• A007481 (program): Number of subsequences of [ 1,…,n ] in which each even number has an odd neighbor.
• A007482 (program): a(n) is the number of subsequences of [ 1, …, 2n ] in which each odd number has an even neighbor.
• A007483 (program): a(n) = 3*a(n-1) + 2*a(n-2), with a(0)=1, a(1)=5.
• A007484 (program): a(n) = 3*a(n-1) + 2*a(n-2), with a(0)=2, a(1)=7.
• A007486 (program): a(n) = a(n-1) + a(n-2) + a(n-3).
• A007487 (program): Sum of 9th powers.
• A007489 (program): a(n) = Sum_{k=1..n} k!.
• A007491 (program): Smallest prime > n^2.
• A007492 (program): Fibonacci(n) - (-1)^n.
• A007493 (program): Decimal expansion of Wallis’ number, the real root of x^3 - 2*x - 5.
• A007494 (program): Numbers that are congruent to 0 or 2 mod 3.
• A007495 (program): Josephus problem: survivors.
• A007496 (program): Numbers n such that the decimal expansions of 2^n and 5^n contain no 0’s (probably 33 is last term).
• A007500 (program): Primes whose reversal in base 10 is also prime (called “palindromic primes” by D. Wells, although that name usually refers to A002385). Also called reversible primes.
• A007501 (program): a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
• A007502 (program): Les Marvin sequence: a(n) = F(n)+(n-1)*F(n-1), F() = Fibonacci numbers.
• A007503 (program): Number of subgroups of dihedral group: sigma(n) + d(n).
• A007504 (program): Sum of the first n primes.
• A007509 (program): Numerator of Sum_{k=0..n} (-1)^k/(2*k+1).
• A007510 (program): Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.
• A007517 (program): a(n) = phi(n) * (sigma(n) - n).
• A007518 (program): a(n) = floor(n*(n+2)*(2*n-1)/8).
• A007519 (program): Primes of form 8n+1, that is, primes congruent to 1 mod 8.
• A007520 (program): Primes == 3 (mod 8).
• A007521 (program): Primes of the form 8k + 5.
• A007522 (program): Primes of the form 8n+7, that is, primes congruent to -1 mod 8.
• A007525 (program): Decimal expansion of log_2 e.
• A007526 (program): a(n) = n(a(n-1) + 1), a(0) = 0.
• A007528 (program): Primes of the form 6k-1.
• A007531 (program): a(n) = n*(n-1)*(n-2) (or n!/(n-3)!).
• A007533 (program): a(n) = (5n+1)^2 + 4n+1.
• A007538 (program): A self-generating sequence: there are a(n) 3’s between successive 2’s.
• A007543 (program): Frequency of n-th largest distance in N times N grid, N > n.
• A007554 (program): Unique attractor for (RIGHT then MOBIUS) transform.
• A007555 (program): Number of standard paths of length n in composition poset.
• A007556 (program): Number of 8-ary trees with n vertices.
• A007559 (program): Triple factorial numbers (3*n-2)!!! with leading 1 added.
• A007564 (program): Shifts left when INVERT transform applied thrice.
• A007566 (program): a(n+1) = (2n+3)*a(n) - 2n*a(n-1) + 8n, a(0) = 1, a(1) = 3.
• A007568 (program): Knopfmacher expansion of 2/3: a(n+1) = a(n-1)(a(n)+1)-1.
• A007570 (program): a(n) = F(F(n)), where F is a Fibonacci number.
• A007572 (program): Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))).
• A007574 (program): Patterns in a dual ring.
• A007581 (program): a(n) = (2^n+1)*(2^n+2)/6.
• A007582 (program): a(n) = 2^(n-1)*(1+2^n).
• A007583 (program): a(n) = (2^(2*n + 1) + 1)/3.
• A007584 (program): 9-gonal (or enneagonal) pyramidal numbers: a(n) = n*(n+1)*(7*n-4)/6.
• A007585 (program): 10-gonal (or decagonal) pyramidal numbers: a(n) = n*(n + 1)*(8*n - 5)/6.
• A007586 (program): 11-gonal (or hendecagonal) pyramidal numbers: n*(n+1)*(3*n-2)/2.
• A007587 (program): 12-gonal (or dodecagonal) pyramidal numbers: n(n+1)(10n-7)/6.
• A007588 (program): Stella octangula numbers: a(n) = n*(2*n^2 - 1).
• A007590 (program): a(n) = floor(n^2/2).
• A007591 (program): Numbers k such that k^2 + 4 is prime.
• A007595 (program): a(n) = C_n / 2 if n is even or ( C_n + C_((n-1)/2) ) / 2 if n is odd, where C = Catalan numbers (A000108).
• A007598 (program): Squared Fibonacci numbers: F(n)^2 where F = A000045.
• A007600 (program): Minimal number of subsets in a separating family for a set of n elements.
• A007601 (program): Positions where A007600 increases.
• A007605 (program): Sum of digits of n-th prime.
• A007606 (program): Take 1, skip 2, take 3, etc.
• A007607 (program): Skip 1, take 2, skip 3, etc.
• A007609 (program): Values taken by the sigma function A000203, listed with multiplicity and in ascending order.
• A007611 (program): a(n) = n! + 2^n.
• A007612 (program): a(n+1) = a(n) + digital root (A010888) of a(n).
• A007613 (program): a(n) = (8^n + 2(-1)^n)/3.
• A007618 (program): a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5.
• A007619 (program): Wilson quotients: ((p-1)! + 1)/p where p is the n-th prime.
• A007623 (program): Integers written in factorial base.
• A007624 (program): Numbers m such that the product of proper divisors of m = m^k, k>1.
• A007634 (program): Numbers n such that n^2 + n + 41 is composite.
• A007635 (program): Primes of form n^2 + n + 17.
• A007636 (program): Numbers k such that k^2 + k + 17 is composite.
• A007637 (program): Primes of form 3n^2-3n+23.
• A007638 (program): Numbers k such that 3*k^2 - 3*k + 23 is composite.
• A007639 (program): Primes of form 2n^2 - 2n + 19.
• A007640 (program): Numbers k such that 2*k^2 - 2*k + 19 is composite.
• A007641 (program): Primes of the form 2*k^2 + 29.
• A007642 (program): Numbers k such that 2*k^2 +29 is composite.
• A007645 (program): Generalized cuban primes: primes of the form x^2 + xy + y^2; or primes of the form x^2 + 3*y^2; or primes == 0 or 1 (mod 3).
• A007652 (program): Final digit of prime(n).
• A007654 (program): Numbers k such that the standard deviation of 1,…,k is an integer.
• A007655 (program): Standard deviation of A007654.
• A007660 (program): a(n) = a(n-1)*a(n-2) + 1 with a(0) = a(1) = 0.
• A007661 (program): Triple factorial numbers a(n) = n!!!, defined by a(n) = n*a(n-3), a(0) = a(1) = 1, a(2) = 2. Sometimes written n!3.
• A007662 (program): Quadruple factorial numbers n!!!!: a(n) = n*a(n-4).
• A007663 (program): Fermat quotients: (2^(p-1)-1)/p, where p=prime(n).
• A007664 (program): Reve’s puzzle: number of moves needed to solve the Towers of Hanoi puzzle with 4 pegs and n disks, according to the Frame-Stewart algorithm.
• A007665 (program): Tower of Hanoi with 5 pegs.
• A007667 (program): The sum of both two and three consecutive squares.
• A007672 (program): a(n) = A002034(n)!/n.
• A007674 (program): Numbers n such that n and n+1 are squarefree.
• A007675 (program): Numbers m such that m, m+1 and m+2 are squarefree.
• A007676 (program): Numerators of convergents to e.
• A007677 (program): Denominators of convergents to e.
• A007679 (program): If n mod 4 = 0 then 2^(n-1)+1 elif n mod 4 = 2 then 2^(n-1)-1 else 2^(n-1).
• A007680 (program): a(n) = (2n+1)*n!.
• A007681 (program): a(n) = (2*n+1)^2*n!.
• A007685 (program): a(n) = Product_{k=1..n} binomial(2*k,k).
• A007689 (program): a(n) = 2^n + 3^n.
• A007692 (program): Numbers that are the sum of 2 nonzero squares in 2 or more ways.
• A007693 (program): Primes p such that 6*p + 1 is also prime.
• A007694 (program): Numbers k such that phi(k) divides k.
• A007696 (program): Quartic (or 4-fold) factorial numbers: a(n) = Product_{k = 0..n-1} (4*k + 1).
• A007698 (program): a(n) = 22*a(n-1) - 3*a(n-2) + 18*a(n-3) - 11*a(n-4). Deviates from A007699 at the 1403rd term.
• A007699 (program): Pisot sequence E(10,219): a(n) = nearest integer to a(n-1)^2 / a(n-2), starting 10, 219, … Deviates from A007698 at 1403rd term.
• A007700 (program): Numbers n such that n, 2n+1, and 4n+3 all prime.
• A007701 (program): a(0) = 0; for n > 0, a(n) = n^n*2^((n-1)^2).
• A007704 (program): a(n+2) = (a(n) - 1)*a(n+1) + 1.
• A007706 (program): a(n) = 1 + coefficient of x^n in Product_{k>=1} (1-x^k) (essentially the expansion of the Dedekind function eta(x)).
• A007715 (program): Number of 5-leaf rooted trees with n levels.
• A007724 (program): Even minus odd extensions of truncated 3 X 2n grid diagram.
• A007728 (program): 5th binary partition function.
• A007729 (program): 6th binary partition function.
• A007730 (program): 7th binary partition function.
• A007733 (program): Period of binary representation of 1/n. Also, multiplicative order of 2 modulo the odd part of n (= A000265(n)).
• A007735 (program): Period of base 4 representation of 1/n.
• A007737 (program): Period of repeating digits of 1/n in base 6.
• A007739 (program): Period of repeating digits of 1/n in base 8.
• A007742 (program): a(n) = n*(4*n+1).
• A007744 (program): Expansion of (1+6*x)/(1-4*x)^(7/2).
• A007745 (program): a(n) = n OR n^2 (applied to binary expansions).
• A007750 (program): Nonnegative integers n such that n^2*(n+1)*(2*n+1)^2*(7*n+1)/36 is a square.
• A007751 (program): Even bisection of A007750.
• A007752 (program): Odd bisection of A007750.
• A007754 (program): Array (a frieze pattern) defined by a(n,k) = (a(n-1,k)*a(n-1,k+1) - 1) / a(n-2,k+1), read by antidiagonals.
• A007757 (program): Dwork-Kontsevich sequence evaluated at 2*n.
• A007758 (program): a(n) = 2^n*n^2.
• A007762 (program): Number of domino tilings of a certain region.
• A007770 (program): Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1.
• A007774 (program): Numbers that are divisible by exactly 2 different primes; numbers n with omega(n) = A001221(n) = 2.
• A007775 (program): Numbers not divisible by 2, 3 or 5.
• A007778 (program): a(n) = n^(n+1).
• A007781 (program): a(n) = (n+1)^(n+1) - n^n for n>0, a(0) = 1.
• A007793 (program): Number of conjugacy classes of compact Cartan subgroups in Sp_{2n}(F), where p>n and the p-adic field F contains all r-th roots of unity for all r <= 2n.
• A007794 (program): Juxtapose pairs of primes (starting at 1).
• A007795 (program): Juxtapose pairs of primes.
• A007798 (program): Expected number of random moves in Tower of Hanoi problem with n disks starting with a randomly chosen position and ending at a position with all disks on the same peg.
• A007800 (program): From a problem in AI planning: a(n) = 4+a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6)-a(n-7), n>7.
• A007805 (program): a(n) = Fibonacci(6*n + 3)/2.
• A007807 (program): A variation on Euclid: a(n)=g(n)-1, where g(0)=0, g(1)=1, g(n+1)=g(n)(g(n-1)+1).
• A007808 (program): Number of directed column-convex polyominoes of height n: a(k+1)=(k+1)*a(k)+(a(1)+…+a(k)).
• A007814 (program): Exponent of highest power of 2 dividing n, a.k.a. the binary carry sequence, the ruler sequence, or the 2-adic valuation of n.
• A007817 (program): Number of abstract simplicial 2-complexes on {1,2,3,…,n+4} which triangulate a Moebius band in such a way that all vertices lie on the boundary and are traversed in the order 1,2,3,… as one goes around the boundary.
• A007818 (program): Maximal number of bonds joining n nodes in simple cubic lattice.
• A007819 (program): a(n) = Sum_{j=1..n} binomial(n^2, j).
• A007820 (program): Stirling numbers of second kind S(2n,n).
• A007821 (program): Primes p such that pi(p) is not prime.
• A007823 (program): A007824(n)/16.
• A007824 (program): a(n) = f(a(n-1)), with f(m) = Sum i*b(i)*2^(i-1), m = Sum b(i)*2^i, and starting value 16.
• A007830 (program): a(n) = (n+3)^n.
• A007831 (program): Number of edge-labeled series-reduced trees with n nodes.
• A007840 (program): Number of factorizations of permutations of n letters into ordered cycles.
• A007843 (program): Least positive integer k for which 2^n divides k!.
• A007844 (program): Least positive integer k for which 3^n divides k!.
• A007845 (program): Least positive integer k for which 5^n divides k!.
• A007851 (program): Number of elements w of the Weyl group D(n) such that the roots sent negative by w span an Abelian subalgebra of the Lie algebra.
• A007852 (program): Antichains in rooted plane trees on n nodes.
• A007854 (program): G.f.: 1/(1 - 3*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.
• A007856 (program): Subtrees in rooted plane trees on n nodes.
• A007857 (program): Number of independent sets in rooted plane trees on n nodes.
• A007858 (program): G.f. is 1 - 1/f(x), where f(x) = 1+x+3*x^2+9*x^3+32*x^4+… is 1/x times g.f. for A063020.
• A007859 (program): Number of matchings in rooted plane trees on n nodes.
• A007862 (program): Number of triangular numbers that divide n.
• A007863 (program): Number of hybrid binary trees with n internal nodes.
• A007868 (program): Number of inverse pairs of elements in symmetric group S_n, or pairs of total orders on n nodes (average of A000085 and A000142).
• A007875 (program): Number of ways of writing n as p*q, with p <= q, gcd(p, q) = 1.
• A007876 (program): a(2n-1) = n*a(2n-2), a(2n) = n*a(2n-1) + 1.
• A007877 (program): Period 4 zigzag sequence: repeat [0,1,2,1].
• A007879 (program): Chimes made by clock striking the hour and half-hour.
• A007882 (program): Number of lattice points inside circle of radius n is 4(a(n)+n)-3.
• A007886 (program): Number of cycles induced by iterating the Gray-coding of an n-bit number: a(n+1) = a(n) + ( 2^n / C_n), where C_n = least power of 2 >= n (C_n is the length of the cycle).
• A007887 (program): a(n) = Fibonacci(n) mod 9.
• A007889 (program): Number of intransitive (or alternating, or Stanley) trees: vertices are [0,n] and for no i<j<k are both (i,j) and (j,k) edges.
• A007891 (program): A Kutz sequence.
• A007892 (program): A Kutz sequence.
• A007893 (program): A Kutz sequence.
• A007895 (program): Number of terms in the Zeckendorf representation of n (write n as a sum of non-consecutive distinct Fibonacci numbers).
• A007899 (program): Coordination sequence for hexagonal close-packing.
• A007900 (program): Coordination sequence for D_4 lattice.
• A007904 (program): Crystal ball sequence for diamond.
• A007907 (program): Concatenation of sequence (1, 2, …, floor((n-1)/2), floor(n/2), floor(n/2)-1, …, 1) for n >= 1.
• A007908 (program): Triangle of the gods: to get a(n), concatenate the decimal numbers 1,2,3,…,n.
• A007909 (program): Expansion of (1-x)/(1-2*x+x^2-2*x^3).
• A007910 (program): Expansion of 1/((1-2*x)*(1+x^2)).
• A007911 (program): a(n) = (n-1)!! - (n-2)!!.
• A007912 (program): Quantum factorials: (n-1)!! - (n-2)!! (mod n).
• A007913 (program): Squarefree part of n: a(n) is the smallest positive number m such that n/m is a square.
• A007916 (program): Numbers that are not perfect powers.
• A007917 (program): Version 1 of the “previous prime” function: largest prime <= n.
• A007918 (program): Least prime >= n (version 1 of the “next prime” function).
• A007920 (program): Smallest number k such that n + k is prime.
• A007921 (program): Numbers that are not the difference of two primes.
• A007923 (program): Lengths increase by 1, digits cycle through positive digits.
• A007925 (program): a(n) = n^(n+1) - (n+1)^n.
• A007928 (program): Numbers containing an even digit.
• A007929 (program): Odd numbers containing an even digit.
• A007931 (program): Numbers that contain only 1’s and 2’s. Nonempty binary strings of length n in lexicographic order.
• A007932 (program): Numbers that contain only 1’s, 2’s and 3’s.
• A007943 (program): Concatenation of sequence (1,3,..,2n-1,2n,2n-2,..,2).
• A007945 (program): Expansion of (2-x-2*x^2)/((1-x)*(1-x+x^2)).
• A007946 (program): a(n) = 6*(2*n+1)! / ((n!)^2*(n+3)).
• A007947 (program): Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.
• A007948 (program): Largest cubefree number dividing n.
• A007949 (program): Greatest k such that 3^k divides n. Or, 3-adic valuation of n.
• A007950 (program): Binary sieve: delete every 2nd number, then every 4th, 8th, etc.
• A007952 (program): Generated by a sieve: keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.
• A007953 (program): Digital sum (i.e., sum of digits) of n; also called digsum(n).
• A007954 (program): Product of decimal digits of n.
• A007955 (program): Product of divisors of n.
• A007956 (program): Product of the proper divisors of n.
• A007957 (program): Numbers that contain an odd digit.
• A007958 (program): Even numbers with at least one odd digit.
• A007961 (program): n written in base where place values are positive squares.
• A007971 (program): INVERTi transform of central trinomial coefficients (A002426).
• A007972 (program): Number of permutations that are 2 “block reversals” away from 12…n.
• A007978 (program): Least non-divisor of n.
• A007979 (program): Expansion of (1+x^2)(1+x^4)/((1-x)^2*(1-x^2)*(1-x^3)).
• A007980 (program): Expansion of (1+x^2)/((1-x)^2*(1-x^3)).
• A007981 (program): Number of nonsplit type 2 metacyclic 2-groups of order 2^n.
• A007983 (program): Number of non-Abelian metacyclic groups of order p^n (p odd).
• A007987 (program): Number of irreducible words of length 2n in the free group with generators x,y such that the total degree of x and the total degree of y both equal zero.
• A007988 (program): Expansion of (x^6-x^5-x^4+2x^2)/((1-x^3)(1-x^2)^2(1-x)).
• A007993 (program): Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.
• A007997 (program): a(n) = ceiling((n-3)(n-4)/6).
• A008000 (program): Coordination sequence T1 for Zeolite Code ABW and ATN.
• A008013 (program): Coordination sequence occurring in Zeolite Codes AFG, CAN, LIO, LOS.
• A008062 (program): a(n) = maximal value of m such that an n X m radar array exists. (A (0,1) matrix A such that any horizontal shift of A overlaps A in at most a single 1.)
• A008084 (program): Coordination sequence T1 for Zeolite Code ACO, ASV, EDI, and THO.
• A008123 (program): Coordination sequence T1 for Zeolite Code KFI.
• A008130 (program): a(n) = floor(n/3)*ceiling(n/3).
• A008133 (program): a(n) = floor(n/3)*floor((n+1)/3).
• A008137 (program): Coordination sequence T1 for Zeolite Code LTA and RHO.
• A008160 (program): Coordination sequence T1 for Zeolite Code MER.
• A008217 (program): a(n) = floor(n/4)*floor((n+1)/4).
• A008218 (program): Floor(n/4)*floor((n+1)/4)*floor((n+2)/4).
• A008233 (program): a(n) = floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4).
• A008238 (program): a(n) = floor(n/4)*ceiling(n/4).
• A008253 (program): Coordination sequence for diamond.
• A008255 (program): Coordination sequence T2 for feldspar.
• A008259 (program): Coordination sequence T2 for Moganite, also for BGB1.
• A008260 (program): Coordination sequence for Paracelsian.
• A008261 (program): Coordination sequence for quartz.
• A008264 (program): Coordination sequence for tridymite, lonsdaleite, and wurtzite.
• A008266 (program): Coordination sequence T1 for Zeolite Code GIS.
• A008269 (program): Number of strings on n symbols in Stockhausen problem.
• A008270 (program): Total length of strings on n symbols in Stockhausen problem.
• A008279 (program): Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.
• A008280 (program): Boustrophedon version of triangle of Euler-Bernoulli or Entringer numbers read by rows.
• A008281 (program): Triangle of Euler-Bernoulli or Entringer numbers read by rows.
• A008282 (program): Triangle of Euler-Bernoulli or Entringer numbers read by rows: T(n,k) is the number of down-up permutations of n+1 starting with k+1.
• A008287 (program): Triangle of quadrinomial coefficients, row n is the sequence of coefficients of (1 + x + x^2 + x^3)^n.
• A008288 (program): Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.
• A008290 (program): Triangle T(n,k) of rencontres numbers (number of permutations of n elements with k fixed points).
• A008291 (program): Triangle of rencontres numbers.
• A008292 (program): Triangle of Eulerian numbers T(n,k) (n >= 1, 1 <= k <= n) read by rows.
• A008297 (program): Triangle of Lah numbers.
• A008310 (program): Triangle of coefficients of Chebyshev polynomials T_n(x).
• A008311 (program): Triangle of expansions of powers of x in terms of Chebyshev polynomials T_n (x).
• A008312 (program): Triangle of coefficients of Chebyshev polynomials U_n(x).
• A008313 (program): Triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
• A008314 (program): Irregular triangle read by rows: one half of the coefficients of the expansion of (2*x)^n in terms of Chebyshev T-polynomials.
• A008315 (program): Catalan triangle read by rows. Also triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
• A008328 (program): Number of divisors of prime(n)-1.
• A008329 (program): Number of divisors of p+1, p prime.
• A008330 (program): phi(p-1), as p runs through the primes.
• A008331 (program): a(n) = phi(prime(n)+1).
• A008332 (program): Sum of divisors of p-1, p prime.
• A008333 (program): Sum of divisors of p+1, p prime.
• A008334 (program): Number of distinct primes dividing p-1, where p = n-th prime.
• A008335 (program): Number of primes dividing p+1 as p runs through the primes.
• A008336 (program): a(n+1) = a(n)/n if n|a(n) else a(n)*n, a(1) = 1.
• A008339 (program): a(1)=1; for n >= 1, a(n+1) = lcm(a(n),n) / gcd(a(n),n).
• A008343 (program): a(1)=1; thereafter a(n+1) = a(n)-n if a(n) >= n otherwise a(n+1) = a(n)+n.
• A008344 (program): a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.
• A008345 (program): a(n+1) = a(n)-b(n+1) if a(n) >= b(n+1) else a(n)+b(n+1), where {b(n)} are the triangular numbers A000217.
• A008346 (program): a(n) = Fibonacci(n) + (-1)^n.
• A008347 (program): a(n) = Sum_{i=0..n-1} (-1)^i * prime(n-i).
• A008348 (program): a(0)=0; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n).
• A008351 (program): a(n) is the concatenation of a(n-1) and a(n-2) with a(1)=1, a(2)=2.
• A008352 (program): a(n) is formed by concatenating a(n-2) and a(n-1), with a(0) = 1, a(1) = 2;
• A008353 (program): 2^n*(2^(n+1) - n - 1).
• A008354 (program): a(n) = (5*n^2 + 1)*n^2 / 6.
• A008355 (program): Coordination sequence for D_5 lattice.
• A008356 (program): Crystal ball sequence for D_5 lattice.
• A008363 (program): a(n) = floor(n/5)*ceiling(n/5).
• A008364 (program): 11-rough numbers: not divisible by 2, 3, 5 or 7.
• A008365 (program): Smallest prime factor is >= 13.
• A008366 (program): Smallest prime factor is >= 17.
• A008368 (program): Number of orbits on points that are at n steps from the origin in the f.c.c. lattice.
• A008369 (program): Number of orbits on points that are at n steps from 0 in D_4 lattice.
• A008380 (program): 4*(2n-1)!*H(2n), where H(n) = Sum 1/i are harmonic numbers.
• A008381 (program): floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5).
• A008382 (program): a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5)*floor((n+4)/5).
• A008383 (program): Coordination sequence for A_4 lattice.
• A008384 (program): Crystal ball sequence for A_4 lattice.
• A008385 (program): Coordination sequence for A_5 lattice.
• A008386 (program): Crystal ball sequence for A_5 lattice.
• A008387 (program): Coordination sequence for A_6 lattice.
• A008388 (program): Crystal ball sequence for A_6 lattice.
• A008389 (program): Coordination sequence for A_7 lattice.
• A008390 (program): Crystal ball sequence for A_7 lattice.
• A008391 (program): Coordination sequence for A_8 lattice.
• A008392 (program): Crystal ball sequence for A_8 lattice.
• A008393 (program): Coordination sequence for A_9 lattice.
• A008394 (program): Crystal ball sequence for A_9 lattice.
• A008395 (program): Coordination sequence for A_10 lattice.
• A008396 (program): Crystal ball sequence for A_10 lattice.
• A008401 (program): Coordination sequence for {E_6}* lattice.
• A008402 (program): Crystal ball sequence for {E_6}* lattice.
• A008410 (program): a(0) = 1, a(n) = 480*sigma_7(n).
• A008412 (program): Coordination sequence for 4-dimensional cubic lattice (points on surface of 4-dimensional cross-polytope).
• A008413 (program): Coordination sequence for 5-dimensional cubic lattice.
• A008414 (program): Coordination sequence for 6-dimensional cubic lattice.
• A008415 (program): Coordination sequence for 7-dimensional cubic lattice.
• A008416 (program): Coordination sequence for 8-dimensional cubic lattice.
• A008417 (program): Crystal ball sequence for 8-dimensional cubic lattice.
• A008418 (program): Coordination sequence for 9-dimensional cubic lattice.
• A008419 (program): Crystal ball sequence for 9-dimensional cubic lattice.
• A008420 (program): Coordination sequence for 10-dimensional cubic lattice.
• A008421 (program): Crystal ball sequence for 10-dimensional cubic lattice.
• A008427 (program): Theta series of {D_8}* lattice.
• A008428 (program): Theta series of D_6 lattice.
• A008429 (program): Theta series of D_7 lattice.
• A008430 (program): Theta series of D_8 lattice.
• A008431 (program): Theta series of D_9 lattice.
• A008432 (program): Theta series of D_10 lattice.
• A008437 (program): Expansion of Jacobi theta constant theta_2^3 /8.
• A008438 (program): Sum of divisors of 2*n + 1.
• A008439 (program): Expansion of Jacobi theta constant theta_2^5 /32.
• A008440 (program): Expansion of Jacobi theta constant theta_2^6 /(64q^(3/2)).
• A008441 (program): Number of ways of writing n as the sum of 2 triangular numbers.
• A008442 (program): Expansion of Jacobi theta constant (theta_2(2z))^2/4.
• A008443 (program): Number of ordered ways of writing n as the sum of 3 triangular numbers.
• A008451 (program): Number of ways of writing n as a sum of 7 squares.
• A008452 (program): Number of ways of writing n as a sum of 9 squares.
• A008453 (program): Number of ways of writing n as a sum of 11 squares.
• A008454 (program): Tenth powers: a(n) = n^10.
• A008455 (program): 11th powers: a(n) = n^11.
• A008456 (program): 12th powers: a(n) = n^12.
• A008457 (program): a(n) = Sum_{ d >= 1, d divides n} (-1)^(n-d)*d^3.
• A008458 (program): Coordination sequence for hexagonal lattice.
• A008459 (program): Square the entries of Pascal’s triangle.
• A008460 (program): Take sum of squares of digits of previous term; start with 6.
• A008461 (program): Take sum of squares of digits of previous term.
• A008462 (program): Take sum of squares of digits of previous term; start with 8.
• A008463 (program): Take sum of squares of digits of previous term; start with 9.
• A008464 (program): a(n) = 2^(2n+3) - 2^n*(n+3).
• A008466 (program): a(n) = 2^n - Fibonacci(n+2).
• A008468 (program): a(n) = n OR n^3 (applied to binary expansions).
• A008472 (program): Sum of the distinct primes dividing n.
• A008473 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j + k_j).
• A008474 (program): If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).
• A008475 (program): If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 0 by convention).
• A008476 (program): If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j).
• A008477 (program): If n = Product (p_j^k_j) then a(n) = Product (k_j^p_j).
• A008480 (program): Number of ordered prime factorizations of n.
• A008482 (program): Coefficients in expansion of (x-1)*(1+x)^(n-1), n > 0.
• A008483 (program): Number of partitions of n into parts >= 3.
• A008485 (program): Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^n.
• A008486 (program): Expansion of (1 + x + x^2)/(1 - x)^2.
• A008487 (program): Expansion of (1-x^5) / (1-x)^5.
• A008488 (program): Expansion of (1-x^6) / (1-x)^6.
• A008489 (program): Expansion of (1-x^7)/(1-x)^7.
• A008490 (program): Expansion of (1-x^8) / (1-x)^8.
• A008491 (program): Expansion of (1-x^9 ) / (1-x)^9.
• A008492 (program): Expansion of (1-x^10) / (1-x)^10.
• A008493 (program): Expansion of (1-x^11) / (1-x)^11.
• A008494 (program): Expansion of (1-x^12) / (1-x)^12.
• A008495 (program): Expansion of (1-x^13) / (1-x)^13.
• A008496 (program): a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5).
• A008497 (program): a(n) = floor(n/5)*floor((n+1)/5).
• A008498 (program): 4-dimensional centered tetrahedral numbers.
• A008499 (program): Number of 5-dimensional centered tetrahedral numbers.
• A008500 (program): 6-dimensional centered tetrahedral numbers.
• A008501 (program): 7-dimensional centered tetrahedral numbers.
• A008502 (program): 8-dimensional centered tetrahedral numbers.
• A008503 (program): 9-dimensional centered tetrahedral numbers.
• A008504 (program): 10-dimensional centered tetrahedral numbers.
• A008505 (program): 11-dimensional centered tetrahedral numbers.
• A008506 (program): 12-dimensional centered tetrahedral numbers.
• A008507 (program): Number of odd composite numbers less than n-th odd prime.
• A008508 (program): Number of odd primes less than n-th odd composite number.
• A008511 (program): Number of points on surface of 4-dimensional cube.
• A008512 (program): Number of points on the surface of 5-dimensional cube.
• A008513 (program): Number of points on surface of 6-dimensional cube.
• A008514 (program): 4-dimensional centered cube numbers.
• A008515 (program): 5-dimensional centered cube numbers.
• A008516 (program): 6-dimensional centered cube numbers.
• A008518 (program): Triangle of Eulerian numbers with rows multiplied by 1 + x.
• A008522 (program): Numbers that contain the letter `t’.
• A008527 (program): Coordination sequence for body-centered tetragonal lattice.
• A008528 (program): Coordination sequence for 4-dimensional RR-centered di-isohexagonal orthogonal lattice.
• A008529 (program): Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.
• A008530 (program): Coordination sequence for 4-dimensional primitive di-isohexagonal orthogonal lattice.
• A008531 (program): Coordination sequence for {A_4}* lattice.
• A008532 (program): Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice.
• A008533 (program): Coordination sequence for {A_5}* lattice.
• A008534 (program): Coordination sequence for {A_6}* lattice.
• A008535 (program): Coordination sequence for {A_7}* lattice.
• A008538 (program): Numbers that contain the letter ‘s’.
• A008539 (program): Numbers that do not contain the letter `s’.
• A008540 (program): Numbers that contain the letter `f’.
• A008541 (program): Numbers that do not contain the letter `f’.
• A008542 (program): Sextuple factorial numbers: Product_{k=0..n-1} (6*k+1).
• A008543 (program): Sextuple factorial numbers: Product_{k=0..n-1} (6*k + 5).
• A008544 (program): Triple factorial numbers: Product_{k=0..n-1} (3*k+2).
• A008545 (program): Quadruple factorial numbers: Product_{k=0..n-1} (4*k + 3).
• A008546 (program): Quintuple factorial numbers: Product_{k = 0..n-1} (5*k + 4).
• A008548 (program): Quintuple factorial numbers: Product_{k=0..n-1} (5*k+1).
• A008549 (program): Number of ways of choosing at most n-1 items from a set of size 2*n+1.
• A008550 (program): Table T(n,k), n>=0 and k>=0, read by antidiagonals: the k-th column given by the k-th Narayana polynomial.
• A008553 (program): Numbers that contain the letter `y’.
• A008556 (program): Triangle of coefficients of Legendre polynomials 2^n P_n (x).
• A008557 (program): Repeatedly convert from decimal to octal.
• A008558 (program): Repeatedly convert from decimal to octal.
• A008560 (program): a(1) = 2; to get a(n), n >= 2, convert a(n-1) from base 3 to base 2.
• A008574 (program): a(0) = 1, thereafter a(n) = 4n.
• A008576 (program): Coordination sequence for planar net 4.8.8.
• A008577 (program): Crystal ball sequence for planar net 4.8.8.
• A008578 (program): Prime numbers at the beginning of the 20th century (today 1 is no longer regarded as a prime).
• A008579 (program): Coordination sequence for planar net 3.6.3.6. Spherical growth function for a certain reflection group in plane.
• A008580 (program): Crystal ball sequence for planar net 3.6.3.6.
• A008581 (program): Molien series for 6-dimensional complex reflection group 4.U_4 (3) of order 2^9 .3^7 .5.7.
• A008583 (program): Molien series for Weyl group E_7.
• A008584 (program): Molien series for Weyl group E_6.
• A008585 (program): a(n) = 3*n.
• A008586 (program): Multiples of 4.
• A008587 (program): Multiples of 5: a(n) = 5 * n.
• A008588 (program): Nonnegative multiples of 6.
• A008589 (program): Multiples of 7.
• A008590 (program): Multiples of 8.
• A008591 (program): Multiples of 9: a(n) = 9*n.
• A008592 (program): Multiples of 10: a(n) = 10 * n.
• A008593 (program): Multiples of 11.
• A008594 (program): Multiples of 12: a(n) = 12*n.
• A008595 (program): Multiples of 13.
• A008596 (program): Multiples of 14.
• A008597 (program): Multiples of 15.
• A008598 (program): Multiples of 16.
• A008599 (program): Multiples of 17.
• A008600 (program): Multiples of 18.
• A008601 (program): Multiples of 19.
• A008602 (program): Multiples of 20.
• A008603 (program): Multiples of 21.
• A008604 (program): Multiples of 22.
• A008605 (program): Multiples of 23.
• A008606 (program): Multiples of 24.
• A008607 (program): Multiples of 25.
• A008609 (program): a(n) = n + max_{0 <= i <n} ((n-i)*a(i)), a(0) = 1.
• A008610 (program): Molien series of 4-dimensional representation of cyclic group of order 4 over GF(2) (not Cohen-Macaulay).
• A008611 (program): a(n) = a(n-3) + 1, with a(0)=a(2)=1, a(1)=0.
• A008612 (program): Molien series of 2-dimensional representation of SL(2,3).
• A008613 (program): Molien series for 3-dimensional representation of A_5.
• A008615 (program): a(n) = floor(n/2) - floor(n/3).
• A008616 (program): Expansion of 1/((1-x^2)(1-x^5)).
• A008617 (program): Expansion of 1/((1-x^2)(1-x^7)).
• A008618 (program): Expansion of 1/((1-x^2)(1-x^9)).
• A008619 (program): Positive integers repeated.
• A008620 (program): Positive integers repeated three times.
• A008621 (program): Expansion of 1/((1-x)*(1-x^4)).
• A008622 (program): Expansion of 1/((1-x^4)*(1-x^6)*(1-x^7)).
• A008624 (program): Expansion of (1+x^3)/((1-x^2)*(1-x^4)) = (1-x+x^2)/((1+x)*(1-x)^2*(1+x^2)).
• A008625 (program): G.f.: (1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^6)*(1-x^7)) (or (1+x^5)(1+x^6)/((1-x^3)*(1-x^4)*(1-x^7))).
• A008627 (program): Molien series for A_4.
• A008628 (program): Molien series for A_5.
• A008630 (program): Molien series for A_7.
• A008636 (program): Number of partitions of n into at most 7 parts.
• A008637 (program): Number of partitions of n into at most 8 parts.
• A008638 (program): Number of partitions of n into at most 9 parts.
• A008639 (program): Number of partitions of n into at most 10 parts.
• A008642 (program): Quarter-squares repeated.
• A008643 (program): Molien series for group of 4 X 4 upper triangular matrices over GF(2).
• A008644 (program): Molien series of 5 X 5 upper triangular matrices over GF( 2 ).
• A008645 (program): Molien series of 6 X 6 upper triangular matrices over GF( 2 ).
• A008646 (program): Molien series for cyclic group of order 5.
• A008647 (program): Expansion of g.f.: (1+x^9)/((1-x^4)*(1-x^6)).
• A008648 (program): Molien series of 3 X 3 upper triangular matrices over GF( 5 ).
• A008649 (program): Molien series of 3 X 3 upper triangular matrices over GF( 3 ).
• A008650 (program): Molien series of 4 X 4 upper triangular matrices over GF( 3 ).
• A008651 (program): Molien series of binary icosahedral group.
• A008652 (program): Molien series for group of 3 X 3 upper triangular matrices over GF( 4 ).
• A008653 (program): Theta series of direct sum of 2 copies of hexagonal lattice.
• A008658 (program): Theta series of direct sum of 2 copies of D_4 lattice in powers of q^2.
• A008666 (program): Expansion of g.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)).
• A008667 (program): Expansion of g.f.: 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).
• A008668 (program): Molien series for 4-dimensional reflection group [3,3,5] of order 14400.
• A008669 (program): Molien series for 4-dimensional complex reflection group of order 7680 (in powers of x^4).
• A008670 (program): Molien series for Weyl group F_4.
• A008671 (program): Expansion of 1/((1-x^2)*(1-x^3)*(1-x^7)).
• A008672 (program): Expansion of 1/((1-x)*(1-x^3)*(1-x^5)).
• A008673 (program): Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)).
• A008674 (program): Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).
• A008675 (program): Expansion of 1/( Product_{j=0..5} (1-x^(2*j+1)) ).
• A008676 (program): Expansion of 1/((1-x^3)*(1-x^5)).
• A008677 (program): Expansion of 1/((1-x^3)*(1-x^5)*(1-x^7)).
• A008678 (program): Expansion of 1/((1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).
• A008679 (program): Expansion of 1/((1-x^3)*(1-x^4)).
• A008680 (program): Expansion of 1/((1-x^3)*(1-x^4)*(1-x^5)).
• A008681 (program): Expansion of 1/((1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)).
• A008682 (program): Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)).
• A008683 (program): Möbius (or Moebius) function mu(n). mu(1) = 1; mu(n) = (-1)^k if n is the product of k different primes; otherwise mu(n) = 0.
• A008687 (program): Number of 1’s in 2’s complement representation of -n.
• A008705 (program): Coefficient of x^n in (Product_{m=1..n}(1-x^m))^n.
• A008706 (program): Coordination sequence for 3.3.3.4.4 planar net.
• A008718 (program): Expansion of g.f.: (1+x^9)/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).
• A008719 (program): Expansion of 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).
• A008720 (program): Molien series for 3-dimensional group [2,5] = *225.
• A008721 (program): Molien series for 3-dimensional group [2,7] = *227.
• A008722 (program): Molien series for 3-dimensional group [2,9] = *229.
• A008723 (program): Molien series for 3-dimensional group [2,11] = *2 2 11.
• A008724 (program): a(n) = floor(n^2/12).
• A008725 (program): Molien series for 3-dimensional group [2,n] = *22n.
• A008726 (program): Molien series 1/((1-x)^2*(1-x^8)) for 3-dimensional group [2,n] = *22n.
• A008727 (program): Molien series for 3-dimensional group [2,n] = *22n.
• A008728 (program): Molien series for 3-dimensional group [2,n ] = *22n.
• A008729 (program): Molien series for 3-dimensional group [2, n] = *22n.
• A008730 (program): Molien series 1/((1-x)^2*(1-x^12)) for 3-dimensional group [2,n] = *22n.
• A008731 (program): Molien series for 3-dimensional group [2, n] = *22n.
• A008732 (program): Molien series for 3-dimensional group [2,n] = *22n.
• A008733 (program): Molien series for 3-dimensional group [2+, n] = 2*(n/2).
• A008734 (program): Molien series for 3-dimensional group [2+,n ] = 2*(n/2).
• A008735 (program): Molien series for 3-dimensional group [2+,n ] = 2*(n/2).
• A008736 (program): Molien series for 3-dimensional group [2+,n] = 2*(n/2).
• A008737 (program): a(n) = floor(n/6)*ceiling(n/6).
• A008738 (program): a(n) = floor((n^2 + 1)/5).
• A008739 (program): Molien series for 3-dimensional group [2+,n] = 2*(n/2).
• A008740 (program): Molien series for 3-dimensional group [2+,n] = 2*(n/2).
• A008742 (program): Molien series for 3-dimensional group [3,3 ]+ = 332.
• A008743 (program): Molien series for 3-dimensional group [3,4]+ = 432.
• A008747 (program): Expansion of (1+x^4)/((1-x)*(1-x^2)*(1-x^3)).
• A008748 (program): Expansion of (1 + x^5) / ((1-x) * (1-x^2) * (1-x^3)) in powers of x.
• A008749 (program): Expansion of (1+x^6)/((1-x)*(1-x^2)*(1-x^3)).
• A008750 (program): Expansion of (1+x^7)/((1-x)*(1-x^2)*(1-x^3)).
• A008751 (program): Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)).
• A008752 (program): Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)).
• A008753 (program): Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)).
• A008754 (program): Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)).
• A008755 (program): Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)).
• A008756 (program): Expansion of (1+x^13)/((1-x)*(1-x^2)*(1-x^3)).
• A008757 (program): Expansion of (1+x^14)/((1-x)*(1-x^2)*(1-x^3)).
• A008758 (program): Expansion of (1+x^15)/((1-x)*(1-x^2)*(1-x^3)).
• A008759 (program): Expansion of (1+x^16)/(1-x)/(1-x^2)/(1-x^3).
• A008760 (program): Expansion of (1+x^17)/((1-x)*(1-x^2)*(1-x^3)).
• A008761 (program): Expansion of (1+x^18)/((1-x)*(1-x^2)*(1-x^3)).
• A008762 (program): Expansion of (1+x)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008763 (program): Expansion of g.f.: x^4/((1-x)*(1-x^2)^2*(1-x^3)).
• A008764 (program): Number of 3 X 3 symmetric stochastic matrices under row and column permutations.
• A008765 (program): Expansion of (1+x^4)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008766 (program): Expansion of (1+x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008767 (program): a(n) = floor(n/7)*ceiling(n/7).
• A008768 (program): Expansion of (1+x^7)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008769 (program): Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008770 (program): Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008771 (program): Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008772 (program): Expansion of (1+x^11)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008773 (program): Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
• A008776 (program): Pisot sequences E(2,6), L(2,6), P(2,6), T(2,6).
• A008778 (program): a(n) = (n+1)*(n^2 +8*n +6)/6. Number of n-dimensional partitions of 4. Number of terms in 4th derivative of a function composed with itself n times.
• A008779 (program): Number of n-dimensional partitions of 5.
• A008780 (program): a(n) = (n-dimensional partitions of 6) + C(n,4) + C(n,3).
• A008784 (program): Numbers n such that sqrt(-1) mod n exists; or, numbers n that are primitively represented by x^2 + y^2.
• A008785 (program): a(n) = (n+4)^n.
• A008786 (program): a(n) = (n+5)^n.
• A008787 (program): a(n) = (n + 6)^n.
• A008788 (program): a(n) = n^(n+2).
• A008789 (program): a(n) = n^(n+3).
• A008790 (program): a(n) = n^(n+4).
• A008791 (program): a(n) = n^(n+5).
• A008794 (program): Squares repeated; a(n) = floor(n/2)^2.
• A008795 (program): Molien series for 3-dimensional representation of dihedral group D_6 of order 6.
• A008796 (program): Molien series for 3-dimensional group [2,3]+ = 223; also for group H_{1,2} of order 384.
• A008797 (program): Molien series for group [2,4]+ = 224.
• A008798 (program): Molien series for group [2,5]+ = 225.
• A008799 (program): Molien series for group [2,6]+ = 226.
• A008800 (program): Molien series for group [2,7]+ = 227.
• A008801 (program): Molien series for group [2,8]+ = 228.
• A008802 (program): Molien series for group [2,9]+ = 229.
• A008803 (program): Molien series for group [2,10]+ = 2 2 10.
• A008804 (program): Expansion of 1/((1-x)^2*(1-x^2)*(1-x^4)).
• A008805 (program): Triangular numbers repeated.
• A008806 (program): Expansion of (1+x^3)/((1-x^2)^2*(1-x^3)).
• A008807 (program): Expansion of (1+x^5)/((1-x^2)^2*(1-x^5)).
• A008808 (program): Expansion of (1+x^7)/((1-x^2)^2*(1-x^7)).
• A008809 (program): Expansion of (1+x^9)/((1-x^2)^2*(1-x^9)).
• A008810 (program): a(n) = ceiling(n^2/3).
• A008811 (program): Expansion of x*(1+x^4)/((1-x)^2*(1-x^4)).
• A008812 (program): Expansion of (1+x^5)/((1-x)^2*(1-x^5)).
• A008813 (program): Expansion of (1+x^6)/((1-x)^2*(1-x^6)).
• A008814 (program): Expansion of (1+x^7)/((1-x)^2*(1-x^7)).
• A008815 (program): Expansion of (1+x^8)/((1-x)^2*(1-x^8)).
• A008816 (program): Expansion of (1+x^9)/((1-x)^2*(1-x^9)).
• A008817 (program): Expansion of (1+x^10)/((1-x)^2*(1-x^10)).
• A008818 (program): Expansion of (1+2*x^3+x^4)/((1-x^2)^2*(1-x^4)); Molien series for 3-dimensional representation of group 2x = [ 2+,4+ ] = CC_4 = C4.
• A008819 (program): Expansion of (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)).
• A008820 (program): Expansion of (1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)).
• A008821 (program): Expansion of (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)).
• A008822 (program): Expansion of (1 + 2*x^2 + x^3)/((1 - x)^2*(1 - x^3)).
• A008823 (program): Expansion of (1+2*x^3+x^5)/((1-x)^2*(1-x^5)).
• A008824 (program): Expansion of (1+2*x^4+x^7)/((1-x)^2*(1-x^7)).
• A008825 (program): Expansion of (1+2*x^5+x^9)/((1-x)^2*(1-x^9)).
• A008827 (program): Coefficients from fractional iteration of exp(x) -1.
• A008830 (program): Discrete logarithm of n to the base 2 modulo 11.
• A008831 (program): Discrete logarithm of n to the base 2 modulo 13.
• A008832 (program): Discrete logarithm of n to the base 2 modulo 19.
• A008833 (program): Largest square dividing n.
• A008834 (program): Largest cube dividing n.
• A008835 (program): Largest 4th power dividing n.
• A008836 (program): Liouville’s function lambda(n) = (-1)^k, where k is number of primes dividing n (counted with multiplicity).
• A008837 (program): a(n) = p*(p-1)/2 for p = prime(n).
• A008838 (program): a(n) = floor(n/8)*ceiling(n/8).
• A008839 (program): Numbers k such that the decimal expansion of 5^k contains no zeros.
• A008843 (program): Squares of NSW numbers (A002315): x^2 such that x^2 - 2y^2 = -1 for some y.
• A008844 (program): Squares of sequence A001653: y^2 such that x^2 - 2*y^2 = -1 for some x.
• A008845 (program): Numbers k such that k+1 and k/2+1 are squares.
• A008846 (program): Hypotenuses of primitive Pythagorean triangles.
• A008851 (program): Congruent to 0 or 1 mod 5.
• A008852 (program): Numbers n such that n^2 and n have same last 2 digits.
• A008854 (program): Numbers that are congruent to {0, 1, 4} mod 5.
• A008857 (program): a(n) = floor(n/9)*ceiling(n/9).
• A008859 (program): a(n) = Sum_{k=0..6} C(n,k).
• A008860 (program): a(n) = Sum_{k=0..7} binomial(n,k).
• A008861 (program): a(n) = Sum_{k=0..8} C(n,k).
• A008862 (program): a(n) = Sum_{k=0..9} C(n,k).
• A008863 (program): a(n) = Sum_{k=0..10} C(n,k).
• A008864 (program): a(n) = prime(n) + 1.
• A008865 (program): a(n) = n^2 - 2.
• A008866 (program): Prime(A052928(n+1)) + (-1)^n* prime(A109613(n)).
• A008867 (program): Triangle of truncated triangular numbers: k-th term in n-th row is number of dots in hexagon of sides k, n-k, k, n-k, k, n-k.
• A008873 (program): 3x+1 sequence starting at 97.
• A008874 (program): 3x+1 sequence starting at 63.
• A008875 (program): 3x+1 sequence starting at 95.
• A008876 (program): 3x+1 sequence starting at 81.
• A008877 (program): 3x+1 sequence starting at 57.
• A008878 (program): 3x+1 sequence starting at 39.
• A008879 (program): 3x+1 sequence starting at 87.
• A008880 (program): 3x + 1 sequence starting at 33.
• A008881 (program): a(n) = Product_{j=0..5} floor((n+j)/6).
• A008882 (program): 3x+1 sequence starting at 99.
• A008883 (program): 3x+1 sequence starting at 51.
• A008884 (program): 3x+1 sequence starting at 27.
• A008885 (program): Aliquot sequence starting at 30.
• A008886 (program): Aliquot sequence starting at 42.
• A008887 (program): Aliquot sequence starting at 60.
• A008891 (program): Aliquot sequence starting at 180.
• A008893 (program): Number of equilateral triangles formed by triples of points taken from a hexagonal chunk of side n in the hexagonal lattice.
• A008894 (program): 3x - 1 sequence starting at 36.
• A008895 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008896 (program): 3x - 1 sequence starting at 66.
• A008897 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008898 (program): Trajectory of 84 under the map x -> x/2 for x even, x -> 3x - 1 for x odd.
• A008899 (program): x -> x/2 if x even, x -> 3x - 1 if x odd.
• A008900 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008901 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008902 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008903 (program): x->x/2 if x even, x->3x-1 if x odd.
• A008904 (program): a(n) is the final nonzero digit of n!.
• A008905 (program): Leading digit of n!.
• A008906 (program): Number of digits in n! excluding final zeros.
• A008908 (program): (1 + number of halving and tripling steps to reach 1 in the Collatz (3x+1) problem), or -1 if 1 is never reached.
• A008909 (program): Join 2n points on a line with n arcs above the line; form graph with the arcs as nodes, joining 2 nodes when the arcs cross. a(n) is the number of cases in which the graph is a path.
• A008911 (program): a(n) = n^2*(n^2 - 1)/6.
• A008912 (program): Truncated triangular numbers (of form n*(n-3)/2 - k^2+k*n+1 for 1<=k<n).
• A008914 (program): Order of simple Chevalley group G_2 (q), q = prime power.
• A008931 (program): Expansion of (2/(1+sqrt(1-36*x)))^(1/3).
• A008935 (program): If 2n = Sum 2^e(k) then a(n) = Sum e(k)^2.
• A008936 (program): Expansion of (1 - 2*x -x^4)/(1 - 2*x)^2 in powers of x.
• A008937 (program): a(n) = Sum_{k=0..n} T(k) where T(n) are the tribonacci numbers A000073.
• A008949 (program): Triangle read by rows of partial sums of binomial coefficients: T(n,k) = Sum_{i=0..k} binomial(n,i) (0 <= k <= n); also dimensions of Reed-Muller codes.
• A008952 (program): Leading digit of 2^n.
• A008953 (program): a(n) is the leading digit of the n-th triangular number, n*(n+1)/2.
• A008954 (program): Final digit of triangular number n*(n+1)/2.
• A008959 (program): Final digit of squares: a(n) = n^2 mod 10.
• A008960 (program): Final digit of cubes: n^3 mod 10.
• A008963 (program): Initial digit of Fibonacci number F(n).
• A008965 (program): Number of necklaces of sets of beads containing a total of n beads.
• A008966 (program): a(n) = 1 if n is squarefree, otherwise 0.
• A008967 (program): Coefficients of Gaussian polynomials q_binomial(n-2, 2). Also triangle of distribution of rank sums: Wilcoxon’s statistic. Irregular triangle read by rows.
• A008973 (program): Fibonacci number F(n) to power F(n).
• A008975 (program): Triangle, read by rows, formed by reading Pascal’s triangle (A007318) mod 10.
• A008977 (program): a(n) = (4*n)!/(n!)^4.
• A008978 (program): a(n) = (5*n)!/(n!)^5.
• A008998 (program): a(n) = 2*a(n-1) + a(n-3), with a(0)=1 and a(1)=2.
• A008999 (program): a(n) = 2*a(n-1) + a(n-4).
• A009000 (program): Ordered hypotenuse numbers (squares are sums of 2 distinct nonzero squares).
• A009001 (program): Expansion of e.g.f: (1+x)*cos(x).
• A009002 (program): Expansion of (1+x)/cos(x).
• A009003 (program): Hypotenuse numbers (squares are sums of 2 nonzero squares).
• A009005 (program): All natural numbers except 1, 2 and 4.
• A009006 (program): Expansion of e.g.f.: 1 + tan(x).
• A009014 (program): Expansion of E.g.f.: (1 + x)/(1 + x + x^2/2).
• A009015 (program): Expansion of E.g.f.: cos(x*cos(x)) (even powers only).
• A009017 (program): Expansion of e.g.f. cos(x*exp(x)).
• A009024 (program): Expansion of e.g.f.: x*cos(log(1+x)).
• A009027 (program): Expansion of cos(log(1+x))/exp(x).
• A009041 (program): Ordered legs of Pythagorean triangles.
• A009042 (program): Expansion of x*cos(sin(x)), odd terms only.
• A009045 (program): Expansion of cos(sin(x))/exp(x).
• A009046 (program): Expansion of cos(sin(x)*cos(x)), even terms only.
• A009056 (program): Numbers >= 3.
• A009061 (program): Expansion of e.g.f. cos(sinh(x)*exp(x)).
• A009070 (program): Ordered sides of Pythagorean triangles.
• A009087 (program): Numbers whose number of divisors is prime (i.e., numbers of the form p^(q-1) for primes p,q).
• A009096 (program): Ordered perimeters of Pythagorean triangles.
• A009097 (program): Expansion of e.g.f. cos(x)*cos(log(1+x)).
• A009101 (program): Fixed point when iterating the function f on n, where f(x) = x + product of digits of x.
• A009102 (program): Expansion of e.g.f. cos(x)/(1+x).
• A009108 (program): Expansion of e.g.f. cos(x)/cosh(log(1+x)).
• A009116 (program): Expansion of e.g.f. cos(x) / exp(x).
• A009117 (program): Expansion of e.g.f.: 1/2 + exp(-4*x)/2.
• A009120 (program): a(n) = (4n)!/(2n)!.
• A009121 (program): Expansion of e.g.f. cosh(exp(x)*x).
• A009124 (program): Expansion of e.g.f. cosh(log(1+sinh(x))).
• A009126 (program): Expansion of e.g.f. cosh(log(1+tanh(x))).
• A009128 (program): Expansion of e.g.f. cosh(log(1+x))*cos(x).
• A009129 (program): Perimeter of more than one Pythagorean triangle.
• A009131 (program): Expansion of e.g.f. cosh(log(1+x))/cosh(x).
• A009132 (program): Expansion of e.g.f. cosh(log(1+x))/exp(x).
• A009152 (program): Expansion of e.g.f. cosh(sinh(x))/exp(x).
• A009153 (program): Expansion of e.g.f. cosh(sinh(x)*exp(x)).
• A009174 (program): Expansion of e.g.f.: cosh(x)*cos(log(1+x)).
• A009175 (program): Expansion of cosh(x)*cos(sin(x)).
• A009177 (program): Numbers that are the hypotenuses of more than one Pythagorean triangle.
• A009178 (program): Expansion of cosh(x)*cosh(log(1+x)).
• A009179 (program): E.g.f. cosh(x)/(1+x).
• A009183 (program): Expansion of e.g.f.: cosh(x)/cosh(log(1+x)).
• A009188 (program): Short leg of more than one Pythagorean triangle.
• A009191 (program): a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).
• A009194 (program): a(n) = gcd(n, sigma(n)).
• A009195 (program): a(n) = gcd(n, phi(n)).
• A009205 (program): a(n) = gcd(d(n), sigma(n)).
• A009213 (program): a(n) = gcd(d(n), phi(n)), where d is the number of divisors of n (A000005) and phi is Euler’s totient function (A000010).
• A009218 (program): Expansion of exp(sinh(log(1+x))).
• A009223 (program): a(n) = gcd(sigma(n), phi(n)).
• A009224 (program): Expansion of exp(sinh(x))*x.
• A009227 (program): Expansion of e.g.f.: exp(sinh(x))/exp(x).
• A009229 (program): Expansion of e.g.f. exp(sinh(x)*cosh(x)).
• A009230 (program): a(n) = lcm(n, d(n)).
• A009233 (program): Expansion of e.g.f. exp(sinh(x)*x) (even powers only).
• A009235 (program): E.g.f. exp( sinh(x) / exp(x) ) = exp( (1-exp(-2*x))/2 ).
• A009236 (program): E.g.f. exp(sinh(x)^2) (even powers only).
• A009242 (program): a(n) = lcm(n, sigma(n)).
• A009262 (program): a(n) = lcm(n, phi(n)).
• A009278 (program): a(n) = lcm(d(n), sigma(n)).
• A009279 (program): a(n) = lcm(d(n), phi(n)).
• A009280 (program): Expansion of exp(x)*cos(log(1+x)).
• A009281 (program): Expansion of exp(x)*cosh(log(1+x)).
• A009283 (program): E.g.f.: exp(x + sinh(x)).
• A009286 (program): a(n) = lcm(sigma(n), phi(n)).
• A009294 (program): Expansion of e.g.f.: exp(x)/cosh(log(1+x)).
• A009306 (program): Expansion of e.g.f.: log(1 + exp(x)*x).
• A009334 (program): E.g.f. log(1+sin(x))*exp(x).
• A009337 (program): Expansion of e.g.f.: log(1+sin(x))/exp(x).
• A009362 (program): Expansion of log(1 + sinh(x)/exp(x)).
• A009383 (program): Expansion of log(1+tanh(log(1+x))).
• A009390 (program): Expansion of e.g.f.: log(1 + tanh(x))*exp(x).
• A009405 (program): Expansion of log(1+x)*cos(log(1+x)).
• A009410 (program): E.g.f. log(1+x)*cos(x).
• A009416 (program): Expansion of e.g.f. log(1+x)*cosh(x).
• A009429 (program): E.g.f. log(1+x)/cos(x).
• A009430 (program): Expansion of log(1+x)/cosh(log(1+x)).
• A009435 (program): Expansion of e.g.f.: log(1+x)/cosh(x).
• A009440 (program): a(n) is the concatenation of n and 6n.
• A009441 (program): a(n) is the concatenation of n and 7n.
• A009444 (program): E.g.f. log(1 + x*exp(-x)).
• A009445 (program): a(n) = (2*n+1)!.
• A009446 (program): E.g.f. sin(x*cos(x)) (odd powers only)
• A009448 (program): E.g.f. sin(x*exp(x)).
• A009454 (program): Expansion of e.g.f. sin(log(1+x)).
• A009455 (program): Expansion of sin(log(1+x))*cos(x).
• A009456 (program): Expansion of sin(log(1+x))*cosh(x).
• A009457 (program): Expansion of sin(log(1+x))*exp(x).
• A009458 (program): Expansion of sin(log(1+x))*log(1+x).
• A009461 (program): Expansion of e.g.f.: sin(log(1+x))/exp(x).
• A009470 (program): a(n) is the concatenation of n and 8n.
• A009474 (program): a(n) is the concatenation of n and 9n.
• A009478 (program): Expansion of sin(sin(x))*x.
• A009481 (program): Expansion of sin(sin(x)*cos(x)).
• A009496 (program): Expansion of e.g.f. sin(sinh(x)*exp(x)).
• A009531 (program): Expansion of the e.g.f. sin(x)*(1+x).
• A009532 (program): Expansion of sin(x)*cos(log(1+x)).
• A009537 (program): Expansion of sin(x)*cosh(log(1+x)).
• A009545 (program): E.g.f. sin(x)*exp(x).
• A009546 (program): Expansion of e.g.f. sin(x)*sin(sin(x)) (even powers only).
• A009551 (program): Expansion of sin(x)/(1-x).
• A009557 (program): Expansion of e.g.f. sin(x)/cosh(log(1+x)).
• A009564 (program): E.g.f. sin(x^2)/2, coefficients of x^(4*n + 2).
• A009565 (program): Expansion of e.g.f. sinh(exp(x)*x).
• A009568 (program): Expansion of e.g.f.: sinh(log(1+sinh(x))).
• A009570 (program): Expansion of e.g.f. sinh(log(1+tanh(x))).
• A009572 (program): Expansion of e.g.f. sinh(log(1+x))*cos(x).
• A009573 (program): Expansion of e.g.f. sinh(log(1+x))*cosh(x).
• A009574 (program): Expansion of e.g.f. sinh(log(1+x))*exp(x).
• A009575 (program): E.g.f. sinh(log(1+x))*log(1+x).
• A009576 (program): Expansion of e.g.f. sinh(log(1+x))/cos(x).
• A009577 (program): Expansion of e.g.f. sinh(log(1+x))/cosh(x).
• A009578 (program): E.g.f. sinh(log(1+x))/exp(x). Unsigned sequence gives degrees of (finite by nilpotent) representations of Braid groups.
• A009598 (program): Expansion of e.g.f. sinh(sinh(x))*exp(x).
• A009599 (program): Expansion of e.g.f. sinh(sinh(x)*exp(x)).
• A009618 (program): Expansion of sinh(x)*cos(log(1+x)).
• A009621 (program): Expansion of sinh(x)*cosh(log(1+x)).
• A009623 (program): Expansion of sinh(x).exp(sinh(x)).
• A009628 (program): Expansion of sinh(x)/(1+x).
• A009632 (program): Expansion of sinh(x)/cosh(log(1+x)).
• A009641 (program): a(n) = Product_{i=0..6} floor((n+i)/7).
• A009661 (program): Smallest number m such that m^m+1 is divisible by n.
• A009694 (program): a(n) = Product_{i=0..7} floor((n+i)/8).
• A009714 (program): a(n) = Product_{i=0..8} floor((n+i)/9).
• A009724 (program): Denominators of Taylor series for 1/(sin x + tan x).
• A009725 (program): Expansion of e.g.f.: tan(x)*(1+x).
• A009731 (program): Expansion of tan(x)*cosh(log(1+x)).
• A009739 (program): E.g.f. tan(x)*exp(x).
• A009744 (program): Expansion of e.g.f. tan(x)*sin(x) (even powers only).
• A009747 (program): E.g.f. tan(x)*sinh(x) (even powers only).
• A009752 (program): Expansion of e.g.f. tan(x)*x (even powers only).
• A009753 (program): Expansion of tan(x)/(1+x).
• A009759 (program): Expansion of (3 - 21*x + 4*x^2)/((x-1)*(x^2 - 6*x + 1)).
• A009764 (program): Tan(x)^2 = sum(n>=0, a(n)*x^(2*n)/(2*n)! ).
• A009766 (program): Catalan’s triangle T(n,k) (read by rows): each term is the sum of the entries above and to the left, i.e., T(n,k) = Sum_{j=0..k} T(n-1,j).
• A009769 (program): Expansion of tanh(log(1+1/x)).
• A009775 (program): Exponential generating function is tanh(log(1+x)).
• A009776 (program): E.g.f.: tanh(log(1+x))*cos(x).
• A009777 (program): E.g.f. tanh(log(1+x))*cosh(x).
• A009778 (program): Expansion of e.g.f.: tanh(log(1+x))*exp(x).
• A009779 (program): Expansion of e.g.f.: tanh(log(1+x))*log(1+x).
• A009782 (program): E.g.f.: expansion of tanh(log(1+x))/exp(x).
• A009832 (program): Expansion of e.g.f. tanh(x)*exp(x).
• A009838 (program): Expansion of e.g.f.: tanh(x)/(1+x).
• A009843 (program): E.g.f. x/cos(x) (odd powers only).
• A009925 (program): Coordination sequence for CaF2(2), F position.
• A009926 (program): Coordination sequence for CaF2(2), Ca position.
• A009940 (program): a(n) = n!*L_{n}(1), where L_{n}(x) is the n-th Laguerre polynomial.
• A009942 (program): Coordination sequence for Ni2In, Position Ni2.
• A009943 (program): Coordination sequence for NiAs(1), As position.
• A009945 (program): Coordination sequence for NiAs(2), As position.
• A009946 (program): Coordination sequence for NiAs(2), Ni position.
• A009947 (program): Sequence of nonnegative integers, but insert n/2 after every even number n.
• A009948 (program): Coordination sequence for alpha-Nd, Position Nd1.
• A009955 (program): Coordination sequence for FeS2-Marcasite, Fe position.
• A009964 (program): Powers of 20.
• A009965 (program): Powers of 21.
• A009966 (program): Powers of 22.
• A009967 (program): Powers of 23.
• A009968 (program): Powers of 24: a(n) = 24^n.
• A009969 (program): Powers of 25.
• A009970 (program): Powers of 26.
• A009971 (program): Powers of 27.
• A009972 (program): Powers of 28.
• A009973 (program): Powers of 29.
• A009974 (program): Powers of 30.
• A009975 (program): Powers of 31: a(n) = 31^n.
• A009976 (program): Powers of 32.
• A009977 (program): Powers of 33.
• A009978 (program): Powers of 34.
• A009979 (program): Powers of 35.
• A009980 (program): Powers of 36.
• A009981 (program): Powers of 37.
• A009982 (program): Powers of 38.
• A009983 (program): Powers of 39.
• A009984 (program): Powers of 40.
• A009985 (program): Powers of 41.
• A009986 (program): Powers of 42.
• A009987 (program): Powers of 43.
• A009988 (program): Powers of 44.
• A009989 (program): Powers of 45.
• A009990 (program): Powers of 46.
• A009991 (program): Powers of 47.
• A009992 (program): Powers of 48: a(n) = 48^n.
• A009994 (program): Numbers with digits in nondecreasing order.
• A009998 (program): Triangle in which j-th entry in i-th row is (j+1)^(i-j).
• A009999 (program): Triangle in which j-th entry in i-th row is (i+1-j)^j, 0<=j<=i.
• A010000 (program): a(0) = 1, a(n) = n^2 + 2 for n > 0.
• A010001 (program): a(0) = 1, a(n) = 5*n^2 + 2 for n>0.
• A010002 (program): a(0) = 1, a(n) = 9*n^2 + 2 for n>0.
• A010003 (program): a(0) = 1, a(n) = 11*n^2 + 2 for n>0.
• A010004 (program): a(0) = 1, a(n) = 13*n^2 + 2 for n>0.
• A010005 (program): a(0) = 1, a(n) = 15*n^2 + 2 for n>0.
• A010006 (program): Coordination sequence for C_3 lattice: a(n) = 16*n^2 + 2 (n>0), a(0)=1.
• A010007 (program): a(0) = 1, a(n) = 17*n^2 + 2 for n>0.
• A010008 (program): a(0) = 1, a(n) = 18*n^2 + 2 for n>0.
• A010009 (program): a(0) = 1, a(n) = 19*n^2 + 2 for n>0.
• A010010 (program): a(0) = 1, a(n) = 20*n^2 + 2 for n>0.
• A010011 (program): a(0) = 1, a(n) = 21*n^2 + 2 for n>0.
• A010012 (program): a(0) = 1, a(n) = 22*n^2 + 2 for n>0.
• A010013 (program): a(0) = 1, a(n) = 23*n^2 + 2 for n>0.
• A010014 (program): a(0) = 1, a(n) = 24*n^2 + 2 for n>0.
• A010015 (program): a(0) = 1, a(n) = 25*n^2 + 2 for n > 0.
• A010016 (program): a(0) = 1, a(n) = 26*n^2 + 2 for n>0.
• A010017 (program): a(0) = 1, a(n) = 27*n^2 + 2 for n>0.
• A010018 (program): a(0) = 1, a(n) = 28*n^2 + 2 for n>0.
• A010019 (program): a(0) = 1, a(n) = 29*n^2 + 2 for n>0.
• A010020 (program): a(0) = 1, a(n) = 31*n^2 + 2 for n>0.
• A010021 (program): a(0) = 1, a(n) = 32*n^2 + 2 for n > 0.
• A010022 (program): a(0) = 1, a(n) = 40*n^2 + 2 for n>0.
• A010023 (program): a(0) = 1, a(n) = 42*n^2 + 2 for n>0.
• A010024 (program): Coordination sequence for squashed {D_5}* lattice, perhaps the smallest example of a “non-superficial” lattice.
• A010025 (program): Crystal ball sequence for squashed {D_5}^* lattice, perhaps the smallest example of a “non-superficial” lattice.
• A010027 (program): Triangle read by rows: T(n,k) is the number of permutations of [n] having k consecutive ascending pairs (0 <= k <= n-1).
• A010035 (program): a(n) = 2*3^(2*n)-3^n.
• A010036 (program): Sum of 2^n, …, 2^(n+1) - 1.
• A010037 (program): Numbers n such that gcd(n^5 + 5, (n+1)^5 + 5) > 1.
• A010049 (program): Second-order Fibonacci numbers.
• A010050 (program): a(n) = (2n)!.
• A010051 (program): Characteristic function of primes: 1 if n is prime, else 0.
• A010052 (program): Characteristic function of squares: a(n) = 1 if n is a square, otherwise 0.
• A010053 (program): a(n) = 4^n*(2*n+1)!*(n!)^2/(n+1).
• A010054 (program): a(n) = 1 if n is a triangular number, otherwise 0.
• A010055 (program): 1 if n is a prime power p^k (k >= 0), otherwise 0.
• A010056 (program): Characteristic function of Fibonacci numbers: a(n) = 1 if n is a Fibonacci number, otherwise 0.
• A010057 (program): a(n) = 1 if n is a cube, else 0.
• A010058 (program): 1 if n is a Catalan number else 0.
• A010059 (program): Another version of the Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 0’s and 1’s.
• A010060 (program): Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 0 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 0’s and 1’s.
• A010061 (program): Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m.
• A010062 (program): a(0)=1; thereafter a(n+1) = a(n) + number of 1’s in binary representation of a(n).
• A010063 (program): a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 1.
• A010064 (program): Base 4 self or Colombian numbers (not of form k + sum of base 4 digits of k).
• A010065 (program): a(n+1) = a(n) + sum of digits in base 4 representation of a(n), with a(0) = 1.
• A010066 (program): a(n+1) = a(n) + sum of digits in base 5 representation of a(n).
• A010068 (program): a(n+1) = a(n) + sum of digits in base 6 representation of a(n).
• A010069 (program): a(n+1) = a(n) + sum of digits in base 7 representation of a(n).
• A010071 (program): a(n+1) = a(n) + sum of digits in base 8 representation of a(n).
• A010072 (program): a(n+1) = a(n) + sum of digits in base 9 representation of a(n).
• A010073 (program): a(n) = sum of base-6 digits of a(n-1) + sum of base-6 digits of a(n-2); a(0)=0, a(1)=1.
• A010074 (program): a(n) = sum of base-7 digits of a(n-1) + sum of base-7 digits of a(n-2).
• A010075 (program): a(n) = sum of base-8 digits of a(n-1) + sum of base-8 digits of a(n-2).
• A010076 (program): a(n) = sum of base-9 digits of a(n-1) + sum of base-9 digits of a(n-2).
• A010077 (program): a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1.
• A010078 (program): Shortest representation of -n in 2’s-complement format.
• A010079 (program): Coordination sequence for net formed by holes in D_4 lattice.
• A010094 (program): Triangle of Euler-Bernoulli or Entringer numbers.
• A010096 (program): log2*(n) (version 1): number of times floor(log_2(x)) is used in floor(log_2(floor(log_2(…(floor(log_2(n)))…)))) = 0.
• A010098 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=3.
• A010099 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=4.
• A010100 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=10.
• A010121 (program): Continued fraction for sqrt(7).
• A010122 (program): Continued fraction for sqrt(13).
• A010123 (program): Continued fraction for sqrt(14).
• A010124 (program): Continued fraction for sqrt(19).
• A010125 (program): Continued fraction for sqrt(21).
• A010126 (program): Continued fraction for sqrt(22).
• A010127 (program): Continued fraction for sqrt(23).
• A010128 (program): Continued fraction for sqrt(29).
• A010129 (program): Continued fraction for sqrt(31).
• A010130 (program): Continued fraction for sqrt(32).
• A010131 (program): Continued fraction for sqrt(33).
• A010132 (program): Continued fraction for sqrt(34).
• A010133 (program): Continued fraction for sqrt(41).
• A010135 (program): Continued fraction for sqrt(45).
• A010137 (program): Continued fraction for sqrt(47).
• A010138 (program): Continued fraction for sqrt(52).
• A010139 (program): Continued fraction for sqrt(53).
• A010140 (program): Continued fraction for sqrt(54).
• A010141 (program): Continued fraction for sqrt(55).
• A010142 (program): Continued fraction for sqrt(57).
• A010143 (program): Continued fraction for sqrt(58).
• A010144 (program): Continued fraction for sqrt(59).
• A010146 (program): Continued fraction for sqrt(62).
• A010148 (program): Continued fraction for sqrt(69).
• A010149 (program): Continued fraction for sqrt(70).
• A010150 (program): Continued fraction for sqrt(71).
• A010152 (program): Continued fraction for sqrt(74).
• A010153 (program): Continued fraction for sqrt(75) (or 5*sqrt(3)).
• A010155 (program): Continued fraction for sqrt(77).
• A010156 (program): Continued fraction for sqrt(78).
• A010157 (program): Continued fraction for sqrt(79).
• A010158 (program): Continued fraction for sqrt(85).
• A010160 (program): Continued fraction for sqrt(88).
• A010161 (program): Continued fraction for sqrt(89).
• A010162 (program): Continued fraction for sqrt(91).
• A010163 (program): Continued fraction for sqrt(92).
• A010164 (program): Continued fraction for sqrt(93).
• A010166 (program): Continued fraction for sqrt(95).
• A010167 (program): Continued fraction for sqrt(96).
• A010169 (program): Continued fraction for sqrt(98).
• A010170 (program): Continued fraction for sqrt(99).
• A010173 (program): Continued fraction for sqrt(107).
• A010174 (program): Continued fraction for sqrt(108).
• A010176 (program): Continued fraction for sqrt(111).
• A010177 (program): Continued fraction for sqrt(112).
• A010178 (program): Continued fraction for sqrt(113).
• A010179 (program): Continued fraction for sqrt(114).
• A010180 (program): Continued fraction for sqrt(115).
• A010182 (program): Continued fraction for sqrt(117).
• A010183 (program): Continued fraction for sqrt(118).
• A010184 (program): Continued fraction for sqrt(119).
• A010186 (program): Continued fraction for sqrt(125).
• A010187 (program): Continued fraction for sqrt(126).
• A010189 (program): Continued fraction for sqrt(128).
• A010191 (program): Continued fraction for sqrt(131).
• A010194 (program): Continued fraction for sqrt(135).
• A010195 (program): Continued fraction for sqrt(136).
• A010196 (program): Continued fraction for sqrt(137).
• A010197 (program): Continued fraction for sqrt(138).
• A010199 (program): Continued fraction for sqrt(140).
• A010200 (program): Continued fraction for sqrt(141).
• A010201 (program): Continued fraction for sqrt(142).
• A010204 (program): Continued fraction for sqrt(153).
• A010207 (program): Continued fraction for sqrt(158).
• A010208 (program): Continued fraction for sqrt(159).
• A010209 (program): Continued fraction for sqrt(160).
• A010211 (program): Continued fraction for sqrt(162).
• A010213 (program): Continued fraction for sqrt(165).
• A010215 (program): Continued fraction for sqrt(167).
• A010217 (program): Continued fraction for sqrt(173).
• A010218 (program): Continued fraction for sqrt(174).
• A010219 (program): Continued fraction for sqrt(175).
• A010220 (program): Continued fraction for sqrt(176).
• A010221 (program): Continued fraction for sqrt(177).
• A010222 (program): Continued fraction for sqrt(178).
• A010225 (program): Continued fraction for sqrt(183).
• A010227 (program): Continued fraction for sqrt(185).
• A010229 (program): Continued fraction for sqrt(187).
• A010230 (program): Continued fraction for sqrt(188).
• A010231 (program): Continued fraction for sqrt(189).
• A010234 (program): Continued fraction for sqrt(192).
• A010236 (program): Continued fraction for sqrt(194).
• A010238 (program): Maximal size of binary code of length n and asymmetric distance 3.
• A010334 (program): Maximal size of binary code of length n and asymmetric distance 4.
• A010362 (program): Class B multi-edge stars with n edges and 2 odd unlabeled roots.
• A010365 (program): Class B multi-edge stars with n edges and 2 odd labeled roots.
• A010368 (program): Number of points of L1 norm 2n in Hamming code version of E_8 lattice.
• A010370 (program): a(n) = binomial(2*n, n)^2 / (1-2*n).
• A010381 (program): Squares mod 19.
• A010384 (program): Squares mod 22.
• A010385 (program): Squares mod 23.
• A010387 (program): Squares mod 25.
• A010388 (program): Squares mod 26.
• A010389 (program): Squares mod 27.
• A010391 (program): Squares mod 29.
• A010392 (program): Squares mod 31.
• A010394 (program): Squares mod 33.
• A010395 (program): Squares mod 34.
• A010396 (program): Squares mod 35.
• A010398 (program): Squares mod 37.
• A010399 (program): Squares mod 38.
• A010400 (program): Squares mod 39.
• A010402 (program): Squares mod 41.
• A010403 (program): Squares mod 42.
• A010404 (program): Squares mod 43.
• A010405 (program): Squares mod 44.
• A010406 (program): Squares mod 45.
• A010407 (program): Squares mod 46.
• A010408 (program): Squares mod 47.
• A010410 (program): Squares mod 49.
• A010411 (program): Squares mod 50.
• A010412 (program): Squares mod 51.
• A010413 (program): Squares mod 52.
• A010414 (program): Squares mod 53.
• A010415 (program): Squares mod 54.
• A010416 (program): Squares mod 55.
• A010417 (program): Squares mod 56.
• A010418 (program): Squares mod 57.
• A010419 (program): Squares mod 58.
• A010420 (program): Squares mod 59.
• A010421 (program): Squares mod 60.
• A010422 (program): Squares mod 61.
• A010423 (program): Squares mod 62.
• A010424 (program): Squares mod 63.
• A010425 (program): Squares mod 64.
• A010426 (program): Squares mod 65.
• A010427 (program): Squares mod 66.
• A010428 (program): Squares mod 67.
• A010429 (program): Squares mod 68.
• A010430 (program): Squares mod 69.
• A010431 (program): Squares mod 70.
• A010433 (program): Squares mod 72.
• A010435 (program): Squares mod 74.
• A010436 (program): Squares mod 75.
• A010437 (program): Squares mod 76.
• A010438 (program): Squares mod 77.
• A010439 (program): Squares mod 78.
• A010440 (program): Squares mod 79.
• A010441 (program): Squares mod 80.
• A010442 (program): Squares mod 81.
• A010443 (program): Squares mod 82.
• A010444 (program): Squares mod 83.
• A010445 (program): Squares mod 84.
• A010446 (program): Squares mod 85.
• A010447 (program): Squares mod 86.
• A010448 (program): Squares mod 87.
• A010449 (program): Squares mod 88.
• A010451 (program): Squares mod 90.
• A010452 (program): Squares mod 91.
• A010453 (program): Squares mod 92.
• A010454 (program): Squares mod 93.
• A010455 (program): Squares mod 94.
• A010456 (program): Squares mod 95.
• A010457 (program): Squares mod 96.
• A010459 (program): Squares mod 98.
• A010460 (program): Squares mod 99.
• A010461 (program): Squares mod 100.
• A010462 (program): Squares mod 30.
• A010464 (program): Decimal expansion of square root of 6.
• A010465 (program): Decimal expansion of square root of 7.
• A010466 (program): Decimal expansion of square root of 8.
• A010467 (program): Decimal expansion of square root of 10.
• A010468 (program): Decimal expansion of square root of 11.
• A010469 (program): Decimal expansion of square root of 12.
• A010470 (program): Decimal expansion of square root of 13.
• A010471 (program): Decimal expansion of square root of 14.
• A010472 (program): Decimal expansion of square root of 15.
• A010473 (program): Decimal expansion of square root of 17.
• A010474 (program): Decimal expansion of square root of 18.
• A010475 (program): Decimal expansion of square root of 19.
• A010476 (program): Decimal expansion of square root of 20.
• A010477 (program): Decimal expansion of square root of 21.
• A010478 (program): Decimal expansion of square root of 22.
• A010479 (program): Decimal expansion of square root of 23.
• A010480 (program): Decimal expansion of square root of 24.
• A010481 (program): Decimal expansion of square root of 26.
• A010482 (program): Decimal expansion of square root of 27.
• A010483 (program): Decimal expansion of square root of 28.
• A010484 (program): Decimal expansion of square root of 29.
• A010485 (program): Decimal expansion of square root of 30.
• A010486 (program): Decimal expansion of square root of 31.
• A010487 (program): Decimal expansion of square root of 32.
• A010488 (program): Decimal expansion of square root of 33.
• A010489 (program): Decimal expansion of square root of 34.
• A010490 (program): Decimal expansion of square root of 35.
• A010491 (program): Decimal expansion of square root of 37.
• A010492 (program): Decimal expansion of square root of 38.
• A010493 (program): Decimal expansion of square root of 39.
• A010494 (program): Decimal expansion of square root of 40.
• A010495 (program): Decimal expansion of square root of 41.
• A010496 (program): Decimal expansion of square root of 42.
• A010497 (program): Decimal expansion of square root of 43.
• A010498 (program): Decimal expansion of square root of 44.
• A010499 (program): Decimal expansion of square root of 45.
• A010500 (program): Decimal expansion of square root of 46.
• A010501 (program): Decimal expansion of square root of 47.
• A010502 (program): Decimal expansion of square root of 48.
• A010503 (program): Decimal expansion of 1/sqrt(2).
• A010504 (program): Decimal expansion of square root of 51.
• A010505 (program): Decimal expansion of square root of 52.
• A010506 (program): Decimal expansion of square root of 53.
• A010507 (program): Decimal expansion of square root of 54.
• A010508 (program): Decimal expansion of square root of 55.
• A010509 (program): Decimal expansion of square root of 56.
• A010510 (program): Decimal expansion of square root of 57.
• A010511 (program): Decimal expansion of square root of 58.
• A010512 (program): Decimal expansion of square root of 59.
• A010513 (program): Decimal expansion of square root of 60.
• A010514 (program): Decimal expansion of square root of 61.
• A010515 (program): Decimal expansion of square root of 62.
• A010516 (program): Decimal expansion of square root of 63.
• A010517 (program): Decimal expansion of square root of 65.
• A010518 (program): Decimal expansion of square root of 66.
• A010519 (program): Decimal expansion of square root of 67.
• A010520 (program): Decimal expansion of square root of 68.
• A010521 (program): Decimal expansion of square root of 69.
• A010522 (program): Decimal expansion of square root of 70.
• A010523 (program): Decimal expansion of square root of 71.
• A010524 (program): Decimal expansion of square root of 72.
• A010525 (program): Decimal expansion of square root of 73.
• A010526 (program): Decimal expansion of square root of 74.
• A010527 (program): Decimal expansion of sqrt(3)/2.
• A010528 (program): Decimal expansion of square root of 76.
• A010529 (program): Decimal expansion of square root of 77.
• A010530 (program): Decimal expansion of square root of 78.
• A010531 (program): Decimal expansion of square root of 79.
• A010532 (program): Decimal expansion of square root of 80.
• A010533 (program): Decimal expansion of square root of 82.
• A010534 (program): Decimal expansion of square root of 83.
• A010535 (program): Decimal expansion of square root of 84.
• A010536 (program): Decimal expansion of square root of 85.
• A010537 (program): Decimal expansion of square root of 86.
• A010538 (program): Decimal expansion of square root of 87.
• A010539 (program): Decimal expansion of square root of 88.
• A010540 (program): Decimal expansion of square root of 89.
• A010541 (program): Decimal expansion of square root of 90.
• A010542 (program): Decimal expansion of square root of 91.
• A010543 (program): Decimal expansion of square root of 92.
• A010544 (program): Decimal expansion of square root of 93.
• A010545 (program): Decimal expansion of square root of 94.
• A010546 (program): Decimal expansion of square root of 95.
• A010547 (program): Decimal expansion of square root of 96.
• A010548 (program): Decimal expansion of square root of 97.
• A010549 (program): Decimal expansion of square root of 98.
• A010550 (program): Decimal expansion of square root of 99.
• A010551 (program): Multiply successively by 1,1,2,2,3,3,4,4,…, n >= 1, a(0) = 1.
• A010552 (program): Multiply successively by 1 (once), 2 (twice), 3 (thrice), etc.
• A010553 (program): a(n) = tau(tau(n)).
• A010554 (program): a(n) = phi(phi(n)), where phi is the Euler totient function.
• A010555 (program): a(n) = 1 if n is the product of an even number of distinct primes, otherwise a(n) = -1.
• A010578 (program): Maximal size of binary code of length n correcting 3 unidirectional errors.
• A010581 (program): Decimal expansion of cube root of 9.
• A010582 (program): Decimal expansion of cube root of 10.
• A010583 (program): Decimal expansion of cube root of 11.
• A010584 (program): Decimal expansion of cube root of 12.
• A010585 (program): Decimal expansion of cube root of 13.
• A010586 (program): Decimal expansion of cube root of 14.
• A010587 (program): Decimal expansion of cube root of 15.
• A010588 (program): Decimal expansion of cube root of 16.
• A010589 (program): Decimal expansion of cube root of 17.
• A010590 (program): Decimal expansion of cube root of 18.
• A010591 (program): Decimal expansion of cube root of 19.
• A010592 (program): Decimal expansion of cube root of 20.
• A010593 (program): Decimal expansion of cube root of 21.
• A010594 (program): Decimal expansion of cube root of 22.
• A010595 (program): Decimal expansion of cube root of 23.
• A010596 (program): Decimal expansion of cube root of 24.
• A010597 (program): Decimal expansion of cube root of 25.
• A010598 (program): Decimal expansion of cube root of 26.
• A010599 (program): Decimal expansion of cube root of 28.
• A010600 (program): Decimal expansion of cube root of 29.
• A010601 (program): Decimal expansion of cube root of 30.
• A010602 (program): Decimal expansion of cube root of 31.
• A010603 (program): Decimal expansion of cube root of 32.
• A010604 (program): Decimal expansion of cube root of 33.
• A010605 (program): Decimal expansion of cube root of 34.
• A010606 (program): Decimal expansion of cube root of 35.
• A010607 (program): Decimal expansion of cube root of 36.
• A010608 (program): Decimal expansion of cube root of 37.
• A010609 (program): Decimal expansion of cube root of 38.
• A010610 (program): Decimal expansion of cube root of 39.
• A010611 (program): Decimal expansion of cube root of 40.
• A010612 (program): Decimal expansion of cube root of 41.
• A010613 (program): Decimal expansion of cube root of 42.
• A010614 (program): Decimal expansion of cube root of 43.
• A010615 (program): Decimal expansion of cube root of 44.
• A010616 (program): Decimal expansion of cube root of 45.
• A010617 (program): Decimal expansion of cube root of 46.
• A010618 (program): Decimal expansion of cube root of 47.
• A010619 (program): Decimal expansion of cube root of 48.
• A010620 (program): Decimal expansion of cube root of 49.
• A010621 (program): Decimal expansion of cube root of 50.
• A010622 (program): Decimal expansion of cube root of 51.
• A010623 (program): Decimal expansion of cube root of 52.
• A010624 (program): Decimal expansion of cube root of 53.
• A010625 (program): Decimal expansion of cube root of 54.
• A010626 (program): Decimal expansion of cube root of 55.
• A010627 (program): Decimal expansion of cube root of 56.
• A010628 (program): Decimal expansion of cube root of 57.
• A010629 (program): Decimal expansion of cube root of 58.
• A010630 (program): Decimal expansion of cube root of 59.
• A010631 (program): Decimal expansion of cube root of 60.
• A010632 (program): Decimal expansion of cube root of 61.
• A010633 (program): Decimal expansion of cube root of 62.
• A010634 (program): Decimal expansion of cube root of 63.
• A010635 (program): Decimal expansion of cube root of 65.
• A010636 (program): Decimal expansion of cube root of 66.
• A010637 (program): Decimal expansion of cube root of 67.
• A010638 (program): Decimal expansion of cube root of 68.
• A010639 (program): Decimal expansion of cube root of 69.
• A010640 (program): Decimal expansion of cube root of 70.
• A010641 (program): Decimal expansion of cube root of 71.
• A010642 (program): Decimal expansion of cube root of 72.
• A010643 (program): Decimal expansion of cube root of 73.
• A010644 (program): Decimal expansion of cube root of 74.
• A010645 (program): Decimal expansion of cube root of 75.
• A010646 (program): Decimal expansion of cube root of 76.
• A010647 (program): Decimal expansion of cube root of 77.
• A010648 (program): Decimal expansion of cube root of 78.
• A010649 (program): Decimal expansion of cube root of 79.
• A010650 (program): Decimal expansion of cube root of 80.
• A010651 (program): Decimal expansion of cube root of 81.
• A010652 (program): Decimal expansion of cube root of 82.
• A010653 (program): Decimal expansion of cube root of 83.
• A010654 (program): Decimal expansion of cube root of 84.
• A010655 (program): Decimal expansion of cube root of 85.
• A010656 (program): Decimal expansion of cube root of 86.
• A010657 (program): Decimal expansion of cube root of 87.
• A010658 (program): Decimal expansion of cube root of 88.
• A010659 (program): Decimal expansion of cube root of 89.
• A010660 (program): Decimal expansion of cube root of 90.
• A010661 (program): Decimal expansion of cube root of 91.
• A010662 (program): Decimal expansion of cube root of 92.
• A010663 (program): Decimal expansion of cube root of 93.
• A010664 (program): Decimal expansion of cube root of 94.
• A010665 (program): Decimal expansion of cube root of 95.
• A010666 (program): Decimal expansion of cube root of 96.
• A010667 (program): Decimal expansion of cube root of 97.
• A010668 (program): Decimal expansion of cube root of 98.
• A010669 (program): Decimal expansion of cube root of 99.
• A010670 (program): Decimal expansion of cube root of 100.
• A010671 (program): Maximal size of binary code of length n correcting 4 unidirectional errors.
• A010673 (program): Period 2: repeat [0, 2].
• A010674 (program): Period 2: repeat (0,3).
• A010675 (program): Period 2: repeat (0,4).
• A010676 (program): Period 2: repeat [0, 5].
• A010677 (program): Period 2: repeat (0,6).
• A010678 (program): Period 2: repeat (0,7).
• A010679 (program): Period 2: repeat (0,8).
• A010680 (program): Decimal expansion of 1/11.
• A010681 (program): Period 2: repeat (0,10).
• A010683 (program): Let S(x,y) = number of lattice paths from (0,0) to (x,y) that use the step set { (0,1), (1,0), (2,0), (3,0), …} and never pass below y = x. Sequence gives S(n-1,n) = number of ‘Schröder’ trees with n+1 leaves and root of degree 2.
• A010684 (program): Period 2: repeat (1,3); offset 0.
• A010685 (program): Period 2: repeat (1,4).
• A010686 (program): Periodic sequence: repeat [1, 5].
• A010687 (program): Repeat (1,6): Period 2.
• A010688 (program): Period 2: repeat (1,7).
• A010689 (program): Periodic sequence: Repeat 1, 8.
• A010690 (program): Period 2: repeat (1,9).
• A010691 (program): Period 2: repeat (1,10).
• A010692 (program): Constant sequence: a(n) = 10.
• A010693 (program): Periodic sequence: Repeat 2,3.
• A010694 (program): Period 2: repeat (2,4).
• A010695 (program): Period 2: repeat (2,5).
• A010696 (program): Periodic sequence: Repeat 2,6.
• A010697 (program): Period 2: repeat (2,7).
• A010698 (program): Period 2: repeat (2,8).
• A010699 (program): Period 2: repeat (2,9).
• A010700 (program): Period 2: repeat (2,10).
• A010701 (program): Constant sequence: the all 3’s sequence.
• A010702 (program): Period 2: repeat (3,4).
• A010703 (program): Period 2: repeat (3,5).
• A010704 (program): Period 2: repeat (3,6).
• A010705 (program): Period 2: repeat (3,7).
• A010706 (program): Period 2: repeat (3,8).
• A010707 (program): Period 2: repeat (3,9).
• A010708 (program): Period 2: repeat (3,10).
• A010709 (program): Constant sequence: the all 4’s sequence.
• A010710 (program): Period 2: repeat (4,5).
• A010711 (program): Period 2: repeat (4,6).
• A010712 (program): Period 2: repeat (4,7).
• A010713 (program): Period 2: repeat (4,8).
• A010714 (program): Period 2: repeat (4,9).
• A010715 (program): Period 2: repeat (4,10).
• A010716 (program): Constant sequence: the all 5’s sequence.
• A010717 (program): Period 2: repeat (5,6).
• A010718 (program): Periodic sequence: repeat [5, 7].
• A010719 (program): Period 2: repeat {5,8}.
• A010720 (program): Period 2: repeat (5,9).
• A010721 (program): Period 2: repeat (5,10).
• A010722 (program): Constant sequence: the all 6’s sequence.
• A010723 (program): Period 2: repeat (6,7).
• A010724 (program): Period 2: repeat (6,8).
• A010725 (program): Period 2: repeat (6,9).
• A010726 (program): Period 2: repeat (6,10).
• A010727 (program): Constant sequence: the all 7’s sequence.
• A010728 (program): Period 2: repeat (7,8).
• A010729 (program): a(n) = 8 - (-1)^n.
• A010730 (program): a(n) = (17 -3*(-1)^n)/2.
• A010731 (program): Constant sequence: the all 8’s sequence.
• A010732 (program): (17-(-1)^n)/2.
• A010733 (program): Period 2: repeat (8,10).
• A010734 (program): Constant sequence: the all 9’s sequence.
• A010735 (program): Period 2: repeat (9,10).
• A010736 (program): Let S(x,y) = number of lattice paths from (0,0) to (x,y) that use the step set { (0,1), (1,0), (2,0), (3,0), ….} and never pass below y = x. Sequence gives S(n-2,n).
• A010737 (program): a(n) = 2*a(n-2) + 1.
• A010738 (program): Shifts 2 places right under binomial transform.
• A010739 (program): Shifts 2 places left under inverse binomial transform.
• A010748 (program): Shifts 4 places right under inverse binomial transform.
• A010749 (program): Shifts 5 places right under inverse binomial transform.
• A010750 (program): Shifts 6 places right under inverse binomial transform.
• A010751 (program): Up once, down twice, up three times, down four times, …
• A010752 (program): Sum along upward diagonal of Pascal triangle to center.
• A010753 (program): Sum along upward diagonal of Pascal triangle up to (but not including) center.
• A010754 (program): Sum along upward diagonal of Pascal triangle to halfway point.
• A010755 (program): Sum along upward diagonal of Pascal triangle up to (but not including) halfway point.
• A010756 (program): Sum along upward diagonal of Pascal triangle from (but not including) center.
• A010757 (program): Sum along upward diagonal of Pascal triangle from center.
• A010758 (program): Sum along upward diagonal of Pascal triangle from (but not including) halfway point.
• A010759 (program): Sum along upward diagonal of Pascal triangle from halfway point.
• A010761 (program): a(n) = floor(n/2) + floor(n/3).
• A010762 (program): a(n) = floor( n/2 ) * floor( n/3 ).
• A010763 (program): a(n) = binomial(2n+1, n+1) - 1.
• A010764 (program): a(n) = floor(n/2) mod floor(n/3).
• A010765 (program): a(n) = floor(n/2)^floor(n/3).
• A010766 (program): Triangle read by rows: row n gives the numbers floor(n/k), k = 1..n.
• A010767 (program): Decimal expansion of 4th root of 2.
• A010768 (program): Decimal expansion of 6th root of 2.
• A010769 (program): Decimal expansion of 7th root of 2.
• A010770 (program): Decimal expansion of 8th root of 2.
• A010771 (program): Decimal expansion of 9th root of 2.
• A010772 (program): Decimal expansion of 10th root of 2.
• A010773 (program): Decimal expansion of 11th root of 2.
• A010774 (program): Decimal expansion of 12th root of 2.
• A010775 (program): Decimal expansion of 13th root of 2.
• A010776 (program): Decimal expansion of 14th root of 2.
• A010783 (program): Triangle of numbers floor(n/(n-k)).
• A010785 (program): Repdigit numbers, or numbers with repeated digits.
• A010786 (program): Floor-factorial numbers: a(n) = Product_{k=1..n} floor(n/k).
• A010790 (program): a(n) = n!*(n+1)!.
• A010791 (program): a(n) = n!*(n+2)!/2.
• A010792 (program): a(n) = n!*(n+3)! / 3!.
• A010793 (program): a(n) = n!*(n+4)! / 4!.
• A010794 (program): a(n) = n!*(n+5)!/5!.
• A010795 (program): a(n) = n!*(n+6)! / 6!.
• A010796 (program): a(n) = n!*(n+1)!/2.
• A010797 (program): n!.(n+1)!.(n+2)! / 2!.3!.
• A010798 (program): n!.(n+1)!.(n+2)!.(n+3)! / 2!.3!.4!.
• A010800 (program): n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)! / 2!*3!*4!*5!*6!.
• A010801 (program): 13th powers: a(n) = n^13.
• A010802 (program): 14th powers: a(n) = n^14.
• A010803 (program): 15th powers: a(n) = n^15.
• A010804 (program): 16th powers: a(n) = n^16.
• A010805 (program): 17th powers: a(n) = n^17.
• A010806 (program): 18th powers: a(n) = n^18.
• A010807 (program): 19th powers: a(n) = n^19.
• A010808 (program): 20th powers: a(n) = n^20.
• A010809 (program): 21st powers: a(n) = n^21.
• A010810 (program): 22nd powers: a(n) = n^22.
• A010811 (program): 23rd powers: a(n) = n^23.
• A010812 (program): 24th powers: a(n) = n^24.
• A010813 (program): 25th powers: a(n) = n^25.
• A010814 (program): Perimeters of integer-sided right triangles.
• A010815 (program): From Euler’s Pentagonal Theorem: coefficient of q^n in Product_{m>=1} (1 - q^m).
• A010816 (program): Expansion of Product_{k>=1} (1 - x^k)^3.
• A010817 (program): Expansion of Product_{k>=1} (1 - x^k)^9.
• A010818 (program): Expansion of Product (1 - x^k)^10 in powers of x.
• A010819 (program): Expansion of Product_{k>=1} (1 - x^k)^11.
• A010820 (program): Expansion of Product_{k>=1} (1 - x^k)^13.
• A010821 (program): Expansion of Product_{k>=1} (1 - x^k)^14.
• A010822 (program): Expansion of Product_{k>=1} (1 - x^k)^15.
• A010823 (program): Expansion of Product_{k>=1} (1 - x^k)^17.
• A010824 (program): Expansion of Product_{k>=1} (1 - x^k)^18.
• A010825 (program): Expansion of Product_{k>=1} (1 - x^k)^19.
• A010826 (program): Expansion of Product_{k>=1} (1 - x^k)^20.
• A010827 (program): Expansion of Product_{k>=1} (1 - x^k)^21.
• A010828 (program): Expansion of Product_{k>=1} (1 - x^k)^22.
• A010829 (program): Expansion of Product_{k>=1} (1 - x^k)^23.
• A010830 (program): Expansion of Product_{k>=1} (1-x^k )^25.
• A010831 (program): Expansion of Product (1-x^k )^26.
• A010832 (program): Expansion of Product_{k>=1} (1-x^k )^27.
• A010833 (program): Expansion of Product (1-x^k )^28.
• A010834 (program): Expansion of Product_{k>=1} (1-x^k )^29.
• A010835 (program): Expansion of Product (1-x^k)^30.
• A010836 (program): Expansion of Product_{k>=1} (1-x^k )^31.
• A010837 (program): Expansion of Product (1-x^k )^32.
• A010838 (program): Expansion of Product (1-x^k )^44.
• A010839 (program): Expansion of Product_{k >= 1} (1-x^k)^48.
• A010840 (program): Expansion of Product (1-x^k )^40.
• A010841 (program): Expansion of Product_{k>=1} (1-x^k)^64.
• A010842 (program): Expansion of e.g.f.: exp(2*x)/(1-x).
• A010843 (program): Incomplete Gamma Function at -3.
• A010844 (program): a(n) = 2*n*a(n-1) + 1 with a(0) = 1.
• A010845 (program): a(n) = 3*n*a(n-1) + 1, a(0) = 1.
• A010846 (program): Number of numbers <= n whose set of prime factors is a subset of the set of prime factors of n.
• A010847 (program): Number of numbers <= n with a prime factor that does not divide n.
• A010848 (program): Number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.
• A010849 (program): Let S(x,y) = number of lattice paths from (0,0) to (x,y) that use the step set { (0,1), (1,0), (2,0), (3,0), ….} and never pass below y = x. Sequence gives S(n-3,n).
• A010850 (program): Constant sequence: a(n) = 11.
• A010851 (program): Constant sequence: a(n) = 12.
• A010852 (program): Constant sequence: a(n) = 13.
• A010853 (program): Constant sequence: a(n) = 14.
• A010854 (program): Constant sequence: a(n) = 15.
• A010855 (program): Constant sequence: a(n) = 16.
• A010856 (program): Constant sequence: a(n) = 17.
• A010857 (program): Constant sequence: a(n) = 18.
• A010858 (program): Constant sequence: a(n) = 19.
• A010859 (program): Constant sequence: a(n) = 20.
• A010860 (program): Constant sequence: a(n) = 21.
• A010861 (program): Constant sequence: a(n) = 22.
• A010862 (program): Constant sequence: a(n) = 23.
• A010863 (program): Constant sequence: a(n) = 24.
• A010864 (program): Constant sequence: a(n) = 25.
• A010865 (program): Constant sequence: a(n) = 26.
• A010866 (program): Constant sequence: a(n) = 27.
• A010867 (program): Constant sequence: a(n) = 28.
• A010868 (program): Constant sequence: a(n) = 29.
• A010869 (program): Constant sequence: a(n) = 30.
• A010870 (program): Constant sequence: a(n) = 31.
• A010871 (program): Constant sequence: a(n) = 32.
• A010872 (program): a(n) = n mod 3.
• A010873 (program): a(n) = n mod 4.
• A010874 (program): a(n) = n mod 5.
• A010875 (program): a(n) = n mod 6.
• A010876 (program): a(n) = n mod 7.
• A010877 (program): a(n) = n mod 8.
• A010878 (program): a(n) = n mod 9.
• A010879 (program): Final digit of n.
• A010880 (program): a(n) = n mod 11.
• A010881 (program): Simple periodic sequence: n mod 12.
• A010882 (program): Period 3: repeat [1, 2, 3].
• A010883 (program): Simple periodic sequence: repeat 1,2,3,4.
• A010884 (program): Period 5: repeat [1,2,3,4,5].
• A010885 (program): Period 6: repeat [1, 2, 3, 4, 5, 6].
• A010886 (program): Period 7: repeat [1, 2, 3, 4, 5, 6, 7].
• A010887 (program): Simple periodic sequence: repeat 1,2,3,4,5,6,7,8.
• A010888 (program): Digital root of n (repeatedly add the digits of n until a single digit is reached).
• A010889 (program): Simple periodic sequence: repeat 1,2,3,4,5,6,7,8,9,10.
• A010891 (program): Inverse of 5th cyclotomic polynomial.
• A010892 (program): Inverse of 6th cyclotomic polynomial. A period 6 sequence.
• A010895 (program): Minimal scope of a (2,n) difference triangle.
• A010900 (program): Pisot sequence E(4,13): a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A010901 (program): Pisot sequences E(4,7), P(4,7).
• A010902 (program): Pisot sequence E(14,23), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
• A010903 (program): Pisot sequence E(3,13): a(n) = floor(a(n-1)^2/a(n-2) + 1/2).
• A010904 (program): Pisot sequence E(4,14): a(n) = floor(a(n-1)^2/a(n-2)+1/2) for n>1, a(0)=4, a(1)=14.
• A010905 (program): Pisot sequence E(4,15): a(n) = floor(a(n-1)^2/a(n-2)+1/2) for n>1, a(0)=4, a(1)=15.
• A010907 (program): Pisot sequence E(4,19), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
• A010908 (program): Pisot sequence E(4,21), a(n) = floor(a(n-1)^2/a(n-2) + 1/2).
• A010909 (program): Pisot sequence E(4,25): a(n) = floor(a(n-1)^2/a(n-2)+1/2) for n>1, a(0)=4, a(1)=25.
• A010910 (program): Pisot sequence E(4,27): a(n) = floor(a(n-1)^2/a(n-2)+1/2) for n>1, a(0)=4, a(1)=27.
• A010911 (program): Pisot sequence E(3,11), a(n) = floor(a(n-1)^2/a(n-2) + 1/2).
• A010912 (program): Pisot sequences E(3,7), P(3,7).
• A010913 (program): Pisot sequence E(3,17), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
• A010914 (program): Pisot sequence E(5,17), a(n) = floor(a(n-1)^2 / a(n-2) + 1/2).
• A010915 (program): Pisot sequence E(6,16), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A010916 (program): Pisot sequence E(8,10), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A010917 (program): Pisot sequence E(5,21), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A010918 (program): Shallit sequence S(8,55): a(n) = floor(a(n-1)^2/a(n-2) + 1).
• A010919 (program): Pisot sequence T(4,13), a(n) = floor(a(n-1)^2/a(n-2)).
• A010920 (program): Pisot sequence T(3,13), a(n) = floor( a(n-1)^2/a(n-2) ).
• A010921 (program): Shallit sequence S(3,13), a(n)=[ a(n-1)^2/a(n-2)+1 ].
• A010922 (program): Pisot sequence T(14,23), a(n)=[ a(n-1)^2/a(n-2) ].
• A010923 (program): Shallit sequence S(14,23), a(n)=[ a(n-1)^2/a(n-2)+1 ].
• A010924 (program): Pisot sequence E(8,55), a(n) = floor(a(n-1)^2/a(n-2) + 1/2).
• A010925 (program): Pisot sequence T(5,21), a(n) = floor( a(n-1)^2/a(n-2) ).
• A010926 (program): Binomial coefficients C(10,n).
• A010927 (program): Binomial coefficient C(11,n).
• A010928 (program): Binomial coefficient C(12,n).
• A010929 (program): Binomial coefficient C(13,n).
• A010930 (program): Binomial coefficient C(14,n).
• A010931 (program): Binomial coefficient C(15,n).
• A010932 (program): Binomial coefficient C(16,n).
• A010933 (program): Binomial coefficient C(17,n).
• A010934 (program): Binomial coefficient C(18,n).
• A010935 (program): Binomial coefficient C(19,n).
• A010936 (program): Binomial coefficient C(20,n).
• A010937 (program): Binomial coefficient C(21,n).
• A010938 (program): Binomial coefficient C(22,n).
• A010939 (program): Binomial coefficient C(23,n).
• A010940 (program): Binomial coefficient C(24,n).
• A010941 (program): Binomial coefficient C(25,n).
• A010942 (program): Binomial coefficient C(26,n).
• A010943 (program): Binomial coefficient C(27,n).
• A010944 (program): Binomial coefficient C(28,n).
• A010945 (program): Binomial coefficient C(29,n).
• A010946 (program): Binomial coefficient C(30,n).
• A010947 (program): Binomial coefficient C(31,n).
• A010948 (program): Binomial coefficient C(32,n).
• A010949 (program): Binomial coefficient C(33,n).
• A010950 (program): Binomial coefficient C(34,n).
• A010951 (program): Binomial coefficient C(35,n).
• A010952 (program): Binomial coefficient C(36,n).
• A010953 (program): Binomial coefficient C(37,n).
• A010954 (program): Binomial coefficient C(38,n).
• A010955 (program): Binomial coefficient C(39,n).
• A010956 (program): Binomial coefficient C(40,n).
• A010957 (program): Binomial coefficient C(41,n).
• A010958 (program): Binomial coefficient C(42,n).
• A010959 (program): Binomial coefficient C(43,n).
• A010960 (program): Binomial coefficient C(44,n).
• A010961 (program): Binomial coefficient C(45,n).
• A010962 (program): Binomial coefficient C(46,n).
• A010963 (program): Binomial coefficient C(47,n).
• A010964 (program): Binomial coefficient C(48,n).
• A010965 (program): a(n) = binomial(n,12).
• A010966 (program): a(n) = binomial(n,13).
• A010967 (program): a(n) = binomial coefficient C(n,14).
• A010968 (program): a(n) = binomial(n,15).
• A010969 (program): a(n) = binomial(n,16).
• A010970 (program): a(n) = binomial(n,17).
• A010971 (program): a(n) = binomial(n,18).
• A010972 (program): a(n) = binomial(n,19).
• A010973 (program): a(n) = binomial(n,20).
• A010974 (program): a(n) = binomial(n,21).
• A010975 (program): a(n) = binomial(n,22).
• A010976 (program): Binomial coefficient C(n,23).
• A010977 (program): a(n) = binomial coefficient C(n,24).
• A010978 (program): a(n) = binomial(n,25).
• A010979 (program): Binomial coefficient C(n,26).
• A010980 (program): a(n) = binomial(n,27).
• A010981 (program): Binomial coefficient C(n,28).
• A010982 (program): Binomial coefficient C(n,29).
• A010983 (program): Binomial coefficient C(n,30).
• A010984 (program): Binomial coefficient C(n,31).
• A010985 (program): Binomial coefficient C(n,32).
• A010986 (program): Binomial coefficient C(n,33).
• A010987 (program): Binomial coefficient C(n,34).
• A010988 (program): Binomial coefficient C(n,35).
• A010989 (program): Binomial coefficient C(n,36).
• A010990 (program): Binomial coefficient C(n,37).
• A010991 (program): Binomial coefficient C(n,38).
• A010992 (program): Binomial coefficient C(n,39).
• A010993 (program): Binomial coefficient C(n,40).
• A010994 (program): a(n) = binomial coefficient C(n,41).
• A010995 (program): Binomial coefficient C(n,42).
• A010996 (program): Binomial coefficient C(n,43).
• A010997 (program): a(n) = binomial coefficient C(n,44).
• A010998 (program): a(n) = binomial coefficient C(n,45).
• A010999 (program): a(n) = binomial coefficient C(n,46).
• A011000 (program): a(n) = binomial coefficient C(n,47).
• A011001 (program): Binomial coefficient C(n,48).
• A011002 (program): Decimal expansion of 4th root of 3.
• A011003 (program): Decimal expansion of 4th root of 5.
• A011004 (program): Decimal expansion of 4th root of 6.
• A011005 (program): Decimal expansion of 4th root of 7.
• A011006 (program): Decimal expansion of 4th root of 8.
• A011007 (program): Decimal expansion of 4th root of 10.
• A011008 (program): Decimal expansion of 4th root of 11.
• A011009 (program): Decimal expansion of 4th root of 12.
• A011010 (program): Decimal expansion of 4th root of 13.
• A011011 (program): Decimal expansion of 4th root of 14.
• A011012 (program): Decimal expansion of 4th root of 15.
• A011013 (program): Decimal expansion of 4th root of 17.
• A011014 (program): Decimal expansion of 4th root of 18.
• A011015 (program): Decimal expansion of 4th root of 19.
• A011016 (program): Decimal expansion of 4th root of 20.
• A011017 (program): Decimal expansion of 4th root of 21.
• A011018 (program): Decimal expansion of 4th root of 22.
• A011019 (program): Decimal expansion of 4th root of 23.
• A011020 (program): Decimal expansion of 4th root of 24.
• A011021 (program): Decimal expansion of 4th root of 26.
• A011022 (program): Decimal expansion of 4th root of 27.
• A011023 (program): Decimal expansion of 4th root of 28.
• A011024 (program): Decimal expansion of 4th root of 29.
• A011025 (program): Decimal expansion of 4th root of 30.
• A011026 (program): Decimal expansion of 4th root of 31.
• A011027 (program): Decimal expansion of 4th root of 32.
• A011028 (program): Decimal expansion of 4th root of 33.
• A011029 (program): Decimal expansion of 4th root of 34.
• A011030 (program): Decimal expansion of 4th root of 35.
• A011031 (program): Decimal expansion of 4th root of 37.
• A011032 (program): Decimal expansion of 4th root of 38.
• A011033 (program): Decimal expansion of 4th root of 39.
• A011034 (program): Decimal expansion of 4th root of 40.
• A011035 (program): Decimal expansion of 4th root of 41.
• A011036 (program): Decimal expansion of 4th root of 42.
• A011037 (program): Decimal expansion of 4th root of 43.
• A011038 (program): Decimal expansion of 4th root of 44.
• A011039 (program): Decimal expansion of 4th root of 45.
• A011040 (program): Decimal expansion of 4th root of 46.
• A011041 (program): Decimal expansion of 4th root of 47.
• A011042 (program): Decimal expansion of 4th root of 48.
• A011043 (program): Decimal expansion of 4th root of 50.
• A011044 (program): Decimal expansion of 4th root of 51.
• A011045 (program): Decimal expansion of 4th root of 52.
• A011046 (program): Decimal expansion of 4th root of 53.
• A011047 (program): Decimal expansion of 4th root of 54.
• A011048 (program): Decimal expansion of 4th root of 55.
• A011049 (program): Decimal expansion of 4th root of 56.
• A011050 (program): Decimal expansion of 4th root of 57.
• A011051 (program): Decimal expansion of 4th root of 58.
• A011052 (program): Decimal expansion of 4th root of 59.
• A011053 (program): Decimal expansion of 4th root of 60.
• A011054 (program): Decimal expansion of 4th root of 61.
• A011055 (program): Decimal expansion of 4th root of 62.
• A011056 (program): Decimal expansion of 4th root of 63.
• A011057 (program): Decimal expansion of 4th root of 65.
• A011058 (program): Decimal expansion of 4th root of 66.
• A011059 (program): Decimal expansion of 4th root of 67.
• A011060 (program): Decimal expansion of 4th root of 68.
• A011061 (program): Decimal expansion of 4th root of 69.
• A011062 (program): Decimal expansion of 4th root of 70.
• A011063 (program): Decimal expansion of 4th root of 71.
• A011064 (program): Decimal expansion of 4th root of 72.
• A011065 (program): Decimal expansion of 4th root of 73.
• A011066 (program): Decimal expansion of 4th root of 74.
• A011067 (program): Decimal expansion of 4th root of 75.
• A011068 (program): Decimal expansion of 4th root of 76.
• A011069 (program): Decimal expansion of 4th root of 77.
• A011070 (program): Decimal expansion of 4th root of 78.
• A011071 (program): Decimal expansion of 4th root of 79.
• A011072 (program): Decimal expansion of 4th root of 80.
• A011073 (program): Decimal expansion of 4th root of 82.
• A011074 (program): Decimal expansion of 4th root of 83.
• A011075 (program): Decimal expansion of 4th root of 84.
• A011076 (program): Decimal expansion of 4th root of 85.
• A011077 (program): Decimal expansion of 4th root of 86.
• A011078 (program): Decimal expansion of 4th root of 87.
• A011079 (program): Decimal expansion of 4th root of 88.
• A011080 (program): Decimal expansion of 4th root of 89.
• A011081 (program): Decimal expansion of 4th root of 90.
• A011082 (program): Decimal expansion of 4th root of 91.
• A011083 (program): Decimal expansion of 4th root of 92.
• A011084 (program): Decimal expansion of 4th root of 93.
• A011085 (program): Decimal expansion of 4th root of 94.
• A011086 (program): Decimal expansion of 4th root of 95.
• A011087 (program): Decimal expansion of 4th root of 96.
• A011088 (program): Decimal expansion of 4th root of 97.
• A011089 (program): Decimal expansion of 4th root of 98.
• A011090 (program): Decimal expansion of 4th root of 99.
• A011091 (program): Decimal expansion of 5th root of 6.
• A011092 (program): Decimal expansion of 5th root of 7.
• A011093 (program): Decimal expansion of 5th root of 8.
• A011094 (program): Decimal expansion of 5th root of 9.
• A011095 (program): Decimal expansion of 5th root of 10.
• A011096 (program): Decimal expansion of 5th root of 11.
• A011097 (program): Decimal expansion of 5th root of 12.
• A011098 (program): Decimal expansion of 5th root of 13.
• A011099 (program): Decimal expansion of 5th root of 14.
• A011100 (program): Decimal expansion of 5th root of 15.
• A011101 (program): Decimal expansion of 5th root of 16.
• A011102 (program): Decimal expansion of 5th root of 17.
• A011103 (program): Decimal expansion of 5th root of 18.
• A011104 (program): Decimal expansion of 5th root of 19.
• A011105 (program): Decimal expansion of 5th root of 20.
• A011106 (program): Decimal expansion of 5th root of 21.
• A011107 (program): Decimal expansion of 5th root of 22.
• A011108 (program): Decimal expansion of 5th root of 23.
• A011109 (program): Decimal expansion of 5th root of 24.
• A011110 (program): Decimal expansion of 5th root of 25.
• A011111 (program): Decimal expansion of 5th root of 26.
• A011112 (program): Decimal expansion of 5th root of 27.
• A011113 (program): Decimal expansion of 5th root of 28.
• A011114 (program): Decimal expansion of 5th root of 29.
• A011115 (program): Decimal expansion of 5th root of 30.
• A011116 (program): Decimal expansion of 5th root of 31.
• A011117 (program): Triangle of numbers S(x,y) = number of lattice paths from (0,0) to (x,y) that use step set { (0,1), (1,0), (2,0), (3,0), ….} and never pass below y = x.
• A011118 (program): Decimal expansion of 5th root of 33.
• A011119 (program): Decimal expansion of 5th root of 34.
• A011120 (program): Decimal expansion of 5th root of 35.
• A011121 (program): Decimal expansion of 5th root of 36.
• A011122 (program): Decimal expansion of 5th root of 37.
• A011123 (program): Decimal expansion of 5th root of 38.
• A011124 (program): Decimal expansion of 5th root of 39.
• A011125 (program): Decimal expansion of 5th root of 40.
• A011126 (program): Decimal expansion of 5th root of 41.
• A011127 (program): Decimal expansion of 5th root of 42.
• A011128 (program): Decimal expansion of 5th root of 43.
• A011129 (program): Decimal expansion of 5th root of 44.
• A011130 (program): Decimal expansion of 5th root of 45.
• A011131 (program): Decimal expansion of 5th root of 46.
• A011132 (program): Decimal expansion of 5th root of 47.
• A011133 (program): Decimal expansion of 5th root of 48.
• A011134 (program): Decimal expansion of 5th root of 49.
• A011135 (program): Decimal expansion of 5th root of 50.
• A011136 (program): Decimal expansion of 5th root of 51.
• A011137 (program): Decimal expansion of 5th root of 52.
• A011138 (program): Decimal expansion of 5th root of 53.
• A011139 (program): Decimal expansion of 5th root of 54.
• A011140 (program): Decimal expansion of 5th root of 55.
• A011141 (program): Decimal expansion of 5th root of 56.
• A011142 (program): Decimal expansion of 5th root of 57.
• A011143 (program): Decimal expansion of 5th root of 58.
• A011144 (program): Decimal expansion of 5th root of 59.
• A011145 (program): Decimal expansion of 5th root of 60.
• A011146 (program): Decimal expansion of 5th root of 61.
• A011147 (program): Decimal expansion of 5th root of 62.
• A011148 (program): Decimal expansion of 5th root of 63.
• A011149 (program): Decimal expansion of 5th root of 64.
• A011150 (program): Decimal expansion of 5th root of 65.
• A011151 (program): Decimal expansion of 5th root of 66.
• A011152 (program): Decimal expansion of 5th root of 67.
• A011153 (program): Decimal expansion of 5th root of 68.
• A011154 (program): Decimal expansion of 5th root of 69.
• A011155 (program): Decimal expansion of 5th root of 70.
• A011156 (program): Decimal expansion of 5th root of 71.
• A011157 (program): Decimal expansion of 5th root of 72.
• A011158 (program): Decimal expansion of 5th root of 73.
• A011159 (program): Decimal expansion of 5th root of 74.
• A011160 (program): Decimal expansion of 5th root of 75.
• A011161 (program): Decimal expansion of 5th root of 76.
• A011162 (program): Decimal expansion of 5th root of 77.
• A011163 (program): Decimal expansion of 5th root of 78.
• A011164 (program): Decimal expansion of 5th root of 79.
• A011165 (program): Decimal expansion of 5th root of 80.
• A011166 (program): Decimal expansion of 5th root of 81.
• A011167 (program): Decimal expansion of 5th root of 82.
• A011168 (program): Decimal expansion of 5th root of 83.
• A011169 (program): Decimal expansion of 5th root of 84.
• A011170 (program): Decimal expansion of 5th root of 85.
• A011171 (program): Decimal expansion of 5th root of 86.
• A011172 (program): Decimal expansion of 5th root of 87.
• A011173 (program): Decimal expansion of 5th root of 88.
• A011174 (program): Decimal expansion of 5th root of 89.
• A011175 (program): Decimal expansion of 5th root of 90.
• A011176 (program): Decimal expansion of 5th root of 91.
• A011177 (program): Decimal expansion of 5th root of 92.
• A011178 (program): Decimal expansion of 5th root of 93.
• A011179 (program): Decimal expansion of 5th root of 94.
• A011180 (program): Decimal expansion of 5th root of 95.
• A011181 (program): Decimal expansion of 5th root of 96.
• A011182 (program): Decimal expansion of 5th root of 97.
• A011183 (program): Decimal expansion of 5th root of 98.
• A011184 (program): Decimal expansion of 5th root of 99.
• A011186 (program): Decimal expansion of 7th root of 4.
• A011188 (program): Decimal expansion of 9th root of 4.
• A011190 (program): Decimal expansion of 11th root of 4.
• A011192 (program): Decimal expansion of 13th root of 4.
• A011195 (program): a(n) = n*(n+1)*(2*n+1)*(3*n+1)/6.
• A011197 (program): a(n) = n*(n+1)*(2*n+1)*(3*n+1)*(4*n+1)/6.
• A011199 (program): a(n) = (n+1)*(2*n+1)*(3*n+1).
• A011200 (program): Decimal expansion of 6th root of 5.
• A011201 (program): Decimal expansion of 7th root of 5.
• A011202 (program): Decimal expansion of 8th root of 5.
• A011203 (program): Decimal expansion of 9th root of 5.
• A011204 (program): Decimal expansion of 10th root of 5.
• A011205 (program): Decimal expansion of 11th root of 5.
• A011206 (program): Decimal expansion of 12th root of 5.
• A011207 (program): Decimal expansion of 13th root of 5.
• A011215 (program): Decimal expansion of 6th root of 6.
• A011216 (program): Decimal expansion of 7th root of 6.
• A011217 (program): Decimal expansion of 8th root of 6.
• A011218 (program): Decimal expansion of 9th root of 6.
• A011219 (program): Decimal expansion of 10th root of 6.
• A011220 (program): Decimal expansion of 11th root of 6.
• A011221 (program): Decimal expansion of 12th root of 6.
• A011222 (program): Decimal expansion of 13th root of 6.
• A011230 (program): Decimal expansion of 6th root of 7.
• A011231 (program): Decimal expansion of 7th root of 7.
• A011232 (program): Decimal expansion of 8th root of 7.
• A011233 (program): Decimal expansion of 9th root of 7.
• A011234 (program): Decimal expansion of 10th root of 7.
• A011235 (program): Decimal expansion of 11th root of 7.
• A011236 (program): Decimal expansion of 12th root of 7.
• A011237 (program): Decimal expansion of 13th root of 7.
• A011245 (program): a(n) = (n+1)*(2*n+1)*(3*n+1)*(4*n+1).
• A011246 (program): Decimal expansion of 7th root of 8.
• A011247 (program): Decimal expansion of 8th root of 8.
• A011248 (program): Twice A000364.
• A011249 (program): Decimal expansion of 10th root of 8.
• A011250 (program): Decimal expansion of 11th root of 8.
• A011252 (program): Decimal expansion of 13th root of 8.
• A011261 (program): Decimal expansion of 7th root of 9.
• A011262 (program): In the prime factorization of n, increment odd powers and decrement even powers (multiplicative and self-inverse).
• A011263 (program): Decimal expansion of 9th root of 9.
• A011264 (program): In the prime factorization of n, increment even powers and decrement odd powers (multiplicative).
• A011265 (program): Decimal expansion of 11th root of 9.
• A011266 (program): a(n) = 2^(n*(n-1)/2)*n!.
• A011267 (program): Decimal expansion of 13th root of 9.
• A011270 (program): Hybrid binary rooted trees with n nodes whose root is labeled by “n”.
• A011275 (program): Decimal expansion of 6th root of 10.
• A011276 (program): Decimal expansion of 7th root of 10.
• A011277 (program): Decimal expansion of 8th root of 10.
• A011278 (program): Decimal expansion of 9th root of 10.
• A011279 (program): Decimal expansion of 10th root of 10.
• A011280 (program): Decimal expansion of 11th root of 10.
• A011281 (program): Decimal expansion of 12th root of 10.
• A011282 (program): Decimal expansion of 13th root of 10.
• A011283 (program): Decimal expansion of 14th root of 10.
• A011290 (program): Decimal expansion of 6th root of 11.
• A011291 (program): Decimal expansion of 7th root of 11.
• A011292 (program): Decimal expansion of 8th root of 11.
• A011293 (program): Decimal expansion of 9th root of 11.
• A011294 (program): Decimal expansion of 10th root of 11.
• A011295 (program): Decimal expansion of 11th root of 11.
• A011296 (program): Decimal expansion of 12th root of 11.
• A011305 (program): Decimal expansion of 6th root of 12.
• A011306 (program): Decimal expansion of 7th root of 12.
• A011307 (program): Decimal expansion of 8th root of 12.
• A011308 (program): Decimal expansion of 9th root of 12.
• A011309 (program): Decimal expansion of 10th root of 12.
• A011310 (program): Decimal expansion of 11th root of 12.
• A011311 (program): Decimal expansion of 12th root of 12.
• A011320 (program): Decimal expansion of 6th root of 13.
• A011321 (program): Decimal expansion of 7th root of 13.
• A011322 (program): Decimal expansion of 8th root of 13.
• A011323 (program): Decimal expansion of 9th root of 13.
• A011324 (program): Decimal expansion of 10th root of 13.
• A011325 (program): Decimal expansion of 11th root of 13.
• A011326 (program): Decimal expansion of 12th root of 13.
• A011327 (program): Decimal expansion of 13th root of 13.
• A011335 (program): Decimal expansion of 6th root of 14.
• A011336 (program): Decimal expansion of 7th root of 14.
• A011337 (program): Decimal expansion of 8th root of 14.
• A011338 (program): Decimal expansion of 9th root of 14.
• A011339 (program): Decimal expansion of 10th root of 14.
• A011340 (program): Decimal expansion of 11th root of 14.
• A011341 (program): Decimal expansion of 12th root of 14.
• A011350 (program): Decimal expansion of 6th root of 15.
• A011351 (program): Decimal expansion of 7th root of 15.
• A011352 (program): Decimal expansion of 8th root of 15.
• A011353 (program): Decimal expansion of 9th root of 15.
• A011354 (program): Decimal expansion of 10th root of 15.
• A011355 (program): Decimal expansion of 11th root of 15.
• A011356 (program): Decimal expansion of 12th root of 15.
• A011357 (program): Decimal expansion of 13th root of 15.
• A011365 (program): Reciprocal of g.f. for A007863.
• A011366 (program): Decimal expansion of 7th root of 16.
• A011367 (program): Expansion of (1-x^2-x^3)/(1-2*x-5*x^2-4*x^3-x^4).
• A011368 (program): Decimal expansion of 9th root of 16.
• A011369 (program): a(n+1) = a(n) - F(n) if > 0, otherwise a(n) + F(n), where F() are Fibonacci numbers; a(0) = 0.
• A011370 (program): Decimal expansion of 11th root of 16.
• A011371 (program): a(n) = n minus (number of 1’s in binary expansion of n). Also highest power of 2 dividing n!.
• A011372 (program): Decimal expansion of 13th root of 16.
• A011373 (program): Number of 1’s in binary expansion of Fibonacci(n).
• A011375 (program): Length of n-th term in A006960.
• A011377 (program): Expansion of 1/((1-x)*(1-2*x)*(1-x^2)).
• A011379 (program): a(n) = n^2*(n+1).
• A011380 (program): Decimal expansion of 6th root of 17.
• A011381 (program): Decimal expansion of 7th root of 17.
• A011382 (program): Decimal expansion of 8th root of 17.
• A011383 (program): Decimal expansion of 9th root of 17.
• A011384 (program): Decimal expansion of 10th root of 17.
• A011385 (program): Decimal expansion of 11th root of 17.
• A011386 (program): Decimal expansion of 12th root of 17.
• A011387 (program): Decimal expansion of 13th root of 17.
• A011395 (program): Decimal expansion of 6th root of 18.
• A011396 (program): Decimal expansion of 7th root of 18.
• A011397 (program): Decimal expansion of 8th root of 18.
• A011398 (program): Decimal expansion of 9th root of 18.
• A011399 (program): Decimal expansion of 10th root of 18.
• A011400 (program): Decimal expansion of 11th root of 18.
• A011401 (program): Decimal expansion of 12th root of 18.
• A011402 (program): Decimal expansion of 13th root of 18.
• A011410 (program): Decimal expansion of 6th root of 19.
• A011411 (program): Decimal expansion of 7th root of 19.
• A011412 (program): Decimal expansion of 8th root of 19.
• A011413 (program): Decimal expansion of 9th root of 19.
• A011414 (program): Decimal expansion of 10th root of 19.
• A011415 (program): Decimal expansion of 11th root of 19.
• A011416 (program): Decimal expansion of 12th root of 19.
• A011417 (program): Decimal expansion of 13th root of 19.
• A011418 (program): Decimal expansion of 14th root of 19.
• A011425 (program): Decimal expansion of 6th root of 20.
• A011426 (program): Decimal expansion of 7th root of 20.
• A011427 (program): Decimal expansion of 8th root of 20.
• A011428 (program): Decimal expansion of 9th root of 20.
• A011429 (program): Decimal expansion of 10th root of 20.
• A011430 (program): Decimal expansion of 11th root of 20.
• A011431 (program): Decimal expansion of 12th root of 20.
• A011446 (program): Decimal expansion of 27th root of 27.
• A011455 (program): Sum 2^Fibonacci(i), i=2..n.
• A011531 (program): Numbers that contain a digit 1 in their decimal representation.
• A011532 (program): Numbers that contain a 2.
• A011533 (program): Numbers that contain a 3.
• A011534 (program): Numbers that contain a 4.
• A011535 (program): Numbers that contain a 5.
• A011536 (program): Numbers that contain a 6.
• A011537 (program): Numbers that contain at least one 7.
• A011538 (program): Numbers that contain an 8.
• A011539 (program): “9ish numbers”: decimal representation contains at least one nine.
• A011540 (program): Numbers that contain a digit 0.
• A011543 (program): Decimal expansion of e truncated to n places.
• A011544 (program): Decimal expansion of e rounded to n places.
• A011545 (program): Decimal expansion of Pi truncated to n places.
• A011546 (program): Decimal expansion of Pi rounded to n places.
• A011547 (program): Decimal expansion of sqrt(2) truncated to n places.
• A011548 (program): Decimal expansion of sqrt(2) rounded to n places.
• A011549 (program): Decimal expansion of sqrt(3) truncated to n places.
• A011550 (program): Decimal expansion of sqrt(3) rounded to n places.
• A011551 (program): Decimal expansion of phi truncated to n places.
• A011552 (program): Decimal expansion of phi rounded to n places.
• A011557 (program): Powers of 10: a(n) = 10^n.
• A011558 (program): Expansion of (x + x^3)/(1 + x + … + x^4) mod 2.
• A011582 (program): Legendre symbol (n,11).
• A011583 (program): Legendre symbol (n,13).
• A011584 (program): Legendre symbol (n,17).
• A011585 (program): Legendre symbol (n,19).
• A011587 (program): Legendre symbol (n,29).
• A011588 (program): Legendre symbol (n,31).
• A011592 (program): Legendre symbol (n,47).
• A011600 (program): Legendre symbol (n,83).
• A011603 (program): Legendre symbol (n,101).
• A011605 (program): Legendre symbol (n,107).
• A011609 (program): Legendre symbol (n,131).
• A011611 (program): Legendre symbol (n,139).
• A011612 (program): Legendre symbol (n,149).
• A011615 (program): Legendre symbol (n,163).
• A011617 (program): Legendre symbol (n,173).
• A011618 (program): Legendre symbol (n,179).
• A011619 (program): Legendre symbol (n,181).
• A011622 (program): Legendre symbol (n,197).
• A011624 (program): Legendre symbol (n,211).
• A011626 (program): Legendre symbol (n,227).
• A011632 (program): 28th cyclotomic polynomial.
• A011634 (program): 35th cyclotomic polynomial.
• A011635 (program): 42nd cyclotomic polynomial.
• A011636 (program): 45th cyclotomic polynomial.
• A011637 (program): 60th cyclotomic polynomial.
• A011638 (program): 63rd cyclotomic polynomial.
• A011639 (program): 65th cyclotomic polynomial.
• A011640 (program): 66th cyclotomic polynomial.
• A011641 (program): 70th cyclotomic polynomial.
• A011642 (program): 77th cyclotomic polynomial.
• A011643 (program): 84th cyclotomic polynomial.
• A011644 (program): 85th cyclotomic polynomial.
• A011645 (program): 90th cyclotomic polynomial.
• A011646 (program): 93rd cyclotomic polynomial.
• A011647 (program): 95th cyclotomic polynomial.
• A011648 (program): 99th cyclotomic polynomial.
• A011649 (program): 102nd cyclotomic polynomial.
• A011652 (program): 114th cyclotomic polynomial.
• A011653 (program): 115th cyclotomic polynomial.
• A011654 (program): 119th cyclotomic polynomial.
• A011655 (program): Period 3: repeat [0, 1, 1].
• A011656 (program): A binary m-sequence: expansion of reciprocal of x^3 + x^2 + 1 (mod 2), shifted by 2 initial 0’s.
• A011657 (program): A binary m-sequence: expansion of reciprocal of x^3 + x + 1 (mod 2, shifted by 2 initial 0’s).
• A011658 (program): Period 5: repeat [0, 0, 0, 1, 1]; also expansion of 1/(x^4 + x^3 + x^2 + x + 1) (mod 2).
• A011659 (program): A binary m-sequence: expansion of reciprocal of x^4+x+1.
• A011660 (program): A binary m-sequence: expansion of reciprocal of x^5+x^4+x^2+x+1.
• A011661 (program): A binary m-sequence: expansion of reciprocal of x^5+x^3+x^2+x+1.
• A011662 (program): A binary m-sequence: expansion of reciprocal of x^5 + x^2 + 1.
• A011663 (program): A binary m-sequence: expansion of reciprocal of x^5+x^4+x^3+x+1.
• A011664 (program): A binary m-sequence: expansion of reciprocal of x^5+x^3+1.
• A011665 (program): A binary m-sequence: expansion of the reciprocal of x^5+x^4+x^3+x^2+1.
• A011666 (program): A binary m-sequence: expansion of reciprocal of x^6+x^5+x^4+x+1.
• A011667 (program): A binary m-sequence: expansion of reciprocal of x^6+x^5+x^3+x^2+1.
• A011668 (program): A binary m-sequence: expansion of reciprocal of x^6+x^5+x^2+x+1.
• A011669 (program): A binary m-sequence: expansion of reciprocal of x^6+x+1.
• A011670 (program): A binary m-sequence: expansion of reciprocal of x^6+x^4+x^3+x+1.
• A011671 (program): A binary m-sequence: expansion of reciprocal of x^6+x^5+x^4+x^2+1.
• A011672 (program): Expansion of reciprocal of x^6+x^3+1 (mod 2).
• A011673 (program): A binary m-sequence: expansion of reciprocal of x^6+x^5+1.
• A011674 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^4+x^3+x^2+1.
• A011675 (program): A binary m-sequence: expansion of reciprocal of x^7+x^4+1.
• A011676 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^4+x^2+1.
• A011677 (program): A binary m-sequence: expansion of reciprocal of x^7+x^5+x^2+x+1.
• A011678 (program): A binary m-sequence: expansion of reciprocal of x^7+x^5+x^3+x+1.
• A011679 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^4+x+1.
• A011680 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^4+x^2+x+1.
• A011681 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^3+x^2+x+1.
• A011682 (program): A binary m-sequence: expansion of reciprocal of x^7+x+1.
• A011683 (program): A binary m-sequence: expansion of reciprocal of x^7+x^5+x^4+x^3+x^2+x+1.
• A011684 (program): A binary m-sequence: expansion of reciprocal of x^7+x^4+x^3+x^2+1.
• A011685 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^3+x+1.
• A011686 (program): A binary m-sequence: expansion of reciprocal of x^7 + x^6 + 1.
• A011687 (program): A binary m-sequence: expansion of reciprocal of x^7 + x^6 + x^5 + x^4 + 1.
• A011688 (program): A binary m-sequence: expansion of reciprocal of x^7+x^5+x^4+x^3+1.
• A011689 (program): A binary m-sequence: expansion of reciprocal of x^7+x^3+x^2+x+1.
• A011690 (program): A binary m-sequence: expansion of reciprocal of x^7+x^3+1.
• A011691 (program): A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^2+1.
• A011692 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^4+x^3+x^2+x+1.
• A011693 (program): A binary m-sequence: expansion of reciprocal of x^8+x^5+x^4+x^3+1.
• A011694 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^3+1.
• A011695 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x^2+1.
• A011696 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x^3+1.
• A011697 (program): A binary m-sequence: expansion of reciprocal of x^8+x^4+x^3+x^2+1.
• A011698 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+x^2+x+1.
• A011699 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x+1.
• A011700 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^3+x+1.
• A011701 (program): A binary m-sequence: expansion of reciprocal of x^8+x^5+x^4+x^3+x^2+x+1.
• A011702 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^4+x^3+x^2+1.
• A011703 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^4+x^3+x^2+1.
• A011704 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^3+x^2+1.
• A011705 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^3+x^2+1.
• A011706 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^2+1.
• A011707 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^4+x^2+x+1.
• A011708 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^3+x^2+x+1.
• A011709 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^2+x+1.
• A011710 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x+1.
• A011711 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^2+x+1.
• A011712 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^4+1.
• A011713 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x+1.
• A011714 (program): A binary m-sequence: expansion of reciprocal of x^8+x^4+x^3+x+1.
• A011715 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+1.
• A011716 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x+1.
• A011717 (program): A binary m-sequence: expansion of reciprocal of x^8+x^5+x^3+x^2+1.
• A011718 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+x^3+x+1.
• A011719 (program): A binary m-sequence: expansion of reciprocal of x^8+x^5+x^3+x+1.
• A011720 (program): A binary m-sequence: expansion of reciprocal of x^8+x^7+x^4+x^3+x^2+x+1.
• A011721 (program): A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^3+1.
• A011722 (program): A binary m-sequence: expansion of reciprocal of x^9+x^4+1.
• A011724 (program): A binary m-sequence: expansion of reciprocal of x^11 + x^2 + 1 (mod 2, shifted by 10 initial 0’s).
• A011746 (program): Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.
• A011747 (program): Expansion of (1 + x^2 + x^4)/(1 + x^2 + x^3 + x^4 + x^5) mod 2.
• A011748 (program): Expansion of (1 + x^2 + x^4)/(1 + x + x^2 + x^4 + x^5) mod 2.
• A011749 (program): Expansion of 1/(1 + x^3 + x^5) mod 2.
• A011750 (program): Expansion of (1 + x^2)/(1 + x + x^2 + x^3 + x^5) mod 2.
• A011751 (program): Expansion of (1 + x^4)/(1 + x + x^3 + x^4 + x^5) mod 2.
• A011754 (program): Number of ones in the binary expansion of 3^n.
• A011755 (program): a(n) = Sum_{k=1..n} k*phi(k).
• A011756 (program): a(n) = prime(n(n+1)/2).
• A011757 (program): a(n) = prime(n^2).
• A011758 (program): Barker sequence of length 13.
• A011759 (program): Barker sequence of length 13.
• A011760 (program): Elevator buttons in U.S.A.: Positive integers except 13.
• A011761 (program): a(n) = a(n-1) + a(n-3), with a(0) = a(1) = 1, a(2) = 5.
• A011763 (program): Days in year in proleptic Gregorian calendar.
• A011765 (program): Period 4: repeat [0, 0, 0, 1].
• A011767 (program): From studying monochromatic solutions to x3-x2=x2-x1+2n.
• A011769 (program): a(0) = 1, a(n+1) = 3 * a(n) - F(n)*(F(n) + 1), where F(n) = A000045(n) is n-th Fibonacci number.
• A011772 (program): Smallest number m such that m(m+1)/2 is divisible by n.
• A011773 (program): Variant of Carmichael’s lambda function: a(p1^e1*…*pN^eN) = lcm((p1-1)*p1^(e1-1), …, (pN-1)*pN^(eN-1)).
• A011776 (program): a(1) = 1; for n > 1, a(n) is defined by the property that n^a(n) divides n! but n^(a(n)+1) does not.
• A011779 (program): Expansion of 1/((1-x)^3*(1-x^3)^2).
• A011780 (program): Expansion of 1/(1-2*x)^3/(1-x^2)^2.
• A011781 (program): Sextuple factorial numbers: a(n) = Product_{k=0..n-1} (6*k+3).
• A011782 (program): Coefficients of expansion of (1-x)/(1-2*x) in powers of x.
• A011785 (program): Number of 3 X 3 matrices whose determinant is 1 mod n.
• A011791 (program): Number of directed animals on a certain lattice.
• A011794 (program): Triangle defined by a(n+1,k)=a(n,k-1)+a(n-1,k), a(n,1)=1, a(1,k)=1, a(2,k)=min(2,k).
• A011795 (program): a(n) = floor(C(n,4)/5).
• A011796 (program): Number of irreducible alternating Euler sums of depth 6 and weight 6+2n.
• A011797 (program): a(n) = floor(C(n,6)/7).
• A011800 (program): Number of labeled forests of n nodes each component of which is a path.
• A011818 (program): Normalized volume of center slice of n-dimensional cube: 2^n* n!*Vol({ (x_1,…,x_n) in [ 0,1 ]^n: n/2 <= Sum_{i = 1..n} x_i <= (n+1)/2 }).
• A011819 (program): M-sequences m_0,m_1,m_2,m_3 with m_1 < n.
• A011826 (program): f-vectors for simplicial complexes of dimension at most 1 (graphs) on at most n-1 vertices.
• A011827 (program): f-vectors for simplicial complexes of dimension at most 2 on at most n-1 vertices.
• A011842 (program): a(n) = floor(n(n-1)(n-2)/24).
• A011843 (program): a(n) = floor(binomial(n,5)/6).
• A011844 (program): [ C(n,7)/8 ].
• A011845 (program): a(n) = floor( binomial(n,8)/9).
• A011846 (program): a(n) = floor( binomial(n,9)/10 ).
• A011847 (program): Triangle of numbers read by rows: T(n,k) = floor( C(n,k)/(k+1) ), where k=0..n-1 and n >= 1.
• A011848 (program): a(n) = floor(binomial(n,2)/2).
• A011849 (program): a(n) = floor(binomial(n,3)/3).
• A011850 (program): a(n) = floor(binomial(n,4)/4).
• A011851 (program): a(n) = floor(binomial(n,5)/5).
• A011852 (program): a(n) = floor(binomial(n,6)/6).
• A011853 (program): [ binomial(n,7)/7 ].
• A011854 (program): a(n) = floor(binomial(n,8)/8).
• A011855 (program): a(n) = floor(binomial(n,9)/9).
• A011856 (program): a(n) = floor(binomial(n,10)/10).
• A011857 (program): Triangle of numbers [ C(n,k)/k ], k=1..n-1.
• A011858 (program): a(n) = floor( n*(n-1)/5 ).
• A011860 (program): Floor( n(n-1)/7 ).
• A011861 (program): a(n) = floor(n(n-1)/8).
• A011862 (program): a(n) = floor(n*(n-1)/9).
• A011863 (program): Nearest integer to (n/2)^4.
• A011864 (program): a(n) = floor(n*(n - 1)/11).
• A011865 (program): a(n) = floor( n*(n - 1)/12 ).
• A011866 (program): a(n) = floor(n*(n-1)/13).
• A011867 (program): a(n) = floor(n*(n-1)/14).
• A011868 (program): a(n) = floor(n*(n-1)/15).
• A011869 (program): a(n) = floor(n*(n-1)/16).
• A011870 (program): a(n) = floor(n*(n-1)/17).
• A011871 (program): [ n(n-1)/18 ].
• A011872 (program): [ n(n-1)/19 ].
• A011873 (program): a(n) = floor(n(n-1)/20).
• A011874 (program): a(n) = floor(n*(n-1)/21).
• A011875 (program): Floor( n*(n-1)/22 ).
• A011876 (program): [ n(n-1)/23 ].
• A011877 (program): a(n) = floor(n*(n-1)/24).
• A011878 (program): a(n) = floor( n(n-1)/25 ).
• A011879 (program): a(n) = floor( n(n-1)/26 ).
• A011880 (program): a(n) = floor(n*(n-1)/27).
• A011881 (program): a(n) = floor(n*(n-1)/28).
• A011882 (program): [ n(n-1)/29 ].
• A011883 (program): a(n) = floor(n*(n-1)/30).
• A011884 (program): Floor(n(n - 1)/31).
• A011885 (program): [ n(n-1)/32 ].
• A011886 (program): a(n) = floor(n*(n-1)*(n-2)/4).
• A011887 (program): [ n(n-1)(n-2)/5 ].
• A011888 (program): Partial sums of A011863.
• A011889 (program): a(n) = floor(n*(n-1)*(n-2)/7).
• A011890 (program): [ n(n-1)(n-2)/8 ].
• A011891 (program): a(n) = floor( n*(n-1)*(n-2)/9 ).
• A011892 (program): [ n(n-1)(n-2)/10 ].
• A011893 (program): [ n(n-1)(n-2)/11 ].
• A011894 (program): a(n) = floor(n(n-1)(n-2)/12).
• A011895 (program): a(n) = floor(n*(n-1)*(n-2)/13).
• A011896 (program): [ n(n-1)(n-2)/14 ].
• A011897 (program): a(n) = floor(n*(n-1)*(n-2)/15).
• A011898 (program): a(n) = floor(n*(n-1)*(n-2)/16).
• A011899 (program): a(n) = floor(n*(n-1)*(n-2)/17).
• A011900 (program): a(n) = 6*a(n-1) - a(n-2) - 2 with a(0) = 1, a(1) = 3.
• A011901 (program): [ n(n-1)(n-2)/19 ].
• A011902 (program): [ n(n-1)(n-2)/20 ].
• A011903 (program): a(n) = floor(n*(n-1)*(n-2)/21).
• A011904 (program): [ n(n-1)(n-2)/22 ].
• A011905 (program): [ n(n-1)(n-2)/23 ].
• A011906 (program): If b(n) is A011900(n) and c(n) is A001109(n), then a(n) = b(n)*c(n) = b(n) + (b(n)+1) + (b(n)+2) + … + c(n).
• A011907 (program): [ n(n-1)(n-2)/25 ].
• A011908 (program): [ n(n-1)(n-2)/26 ].
• A011909 (program): a(n) = floor( n*(n-1)*(n-2)/27 ).
• A011910 (program): Floor( n(n-1)(n-2)/28 ).
• A011911 (program): [ n(n-1)(n-2)/29 ].
• A011912 (program): a(n) = floor(n(n-1)(n-2)/30).
• A011913 (program): a(n) = floor(n*(n - 1)*(n - 2)/31).
• A011914 (program): a(n) = floor(n*(n - 1)*(n - 2)/32).
• A011915 (program): a(n) = floor(n(n-1)(n-2)(n-3)/5).
• A011916 (program): a(n) = ((b(n)-1)+sqrt(3*b(n)^2-4*b(n)+1))/2, where b(n) is A011922(n).
• A011917 (program): [ n(n-1)(n-2)(n-3)/7 ].
• A011918 (program): a(n) = A011916(n) + A011922(n) - 1.
• A011919 (program): a(n) = floor(n*(n-1)*(n-2)*(n-3)/9).
• A011920 (program): a(n) = b(n)*(b(n)+1) = b(n) + … + c(n), where b(n) = A011916(n), c(n) = A011918(n).
• A011921 (program): [ n(n-1)(n-2)(n-3)/11 ].
• A011922 (program): a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3).
• A011923 (program): [ n(n-1)(n-2)(n-3)/13 ].
• A011924 (program): Floor[n(n-1)(n-2)(n-3)/14].
• A011925 (program): a(n) = floor(n*(n-1)*(n-2)*(n-3)/15).
• A011926 (program): a(n) = floor(n*(n-1)*(n-2)*(n-3)/16).
• A011927 (program): [ n(n-1)(n-2)(n-3)/17 ].
• A011928 (program): a(n) = floor(n(n-1)(n-2)(n-3)/18).
• A011929 (program): a(n) = floor(n(n-1)(n-2)(n-3)/19).
• A011930 (program): a(n) = floor(n(n-1)(n-2)(n-3)/20).
• A011931 (program): a(n) = floor(n*(n-1)*(n-2)*(n-3)/21).
• A011932 (program): [ n(n-1)(n-2)(n-3)/22 ].
• A011933 (program): a(n) = floor( n*(n-1)*(n-2)*(n-3)/23 ).
• A011934 (program): a(n) = |1^3 - 2^3 + 3^3 - 4^3 + … + (-1)^(n+1)*n^3|.
• A011935 (program): [ n(n-1)(n-2)(n-3)/25 ].
• A011936 (program): a(n) = floor( n(n-1)(n-2)(n-3)/26 ).
• A011937 (program): [ n(n-1)(n-2)(n-3)/27 ].
• A011938 (program): a(n) = floor( n*(n-1)*(n-2)*(n-3)/28 ).
• A011939 (program): [ n(n-1)(n-2)(n-3)/29 ].
• A011940 (program): a(n) = floor(n(n-1)(n-2)(n-3)/30).
• A011941 (program): a(n) = floor(n*(n-1)*(n-2)*(n-3)/31).
• A011942 (program): [ n(n-1)(n-2)(n-3)/32 ].
• A011943 (program): Numbers k such that any group of k consecutive integers has integral standard deviation (viz. A011944(k)).
• A011944 (program): a(n) = 14*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.
• A011945 (program): Areas of almost-equilateral Heronian triangles (integral side lengths m-1, m, m+1 and integral area).
• A011946 (program): Number of Barlow packings with group P63/mmc(S) that repeat after 4n layers.
• A011947 (program): Number of Barlow packings with group P63/mmc(O) that repeat after 4n+2 layers.
• A011960 (program): Number of ferrites M_2Y_n that repeat after 6n+10 layers.
• A011965 (program): Second differences of Bell numbers.
• A011966 (program): Third differences of Bell numbers.
• A011967 (program): 4th differences of Bell numbers.
• A011968 (program): Apply (1+Shift) to Bell numbers.
• A011969 (program): Apply (1+Shift)^2 to Bell numbers.
• A011970 (program): Apply (1+Shift)^3 to Bell numbers.
• A011971 (program): Aitken’s array: triangle of numbers {a(n,k), n >= 0, 0 <= k <= n} read by rows, defined by a(0,0)=1, a(n,0) = a(n-1,n-1), a(n,k) = a(n,k-1) + a(n-1,k-1).
• A011972 (program): Sequence formed by reading rows of triangle defined in A011971.
• A011973 (program): Irregular triangle of numbers read by rows: {binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2)}; or, triangle of coefficients of (one version of) Fibonacci polynomials.
• A011974 (program): 2 followed by the numbers that are the sum of 2 successive primes.
• A011975 (program): Covering numbers C(n,3,2).
• A011978 (program): Covering numbers C(n,6,2) (next term is <= 15).
• A012000 (program): Expansion of 1/sqrt(1 - 4*x + 16*x^2).
• A012007 (program): cosh(log(cos(x))) = 1+3/4!*x^4+30/6!*x^6+693/8!*x^8+25260/10!*x^10…
• A012019 (program): E.g.f.: exp(sin(arctan(x))).
• A012020 (program): Expansion of e.g.f.: sin(sin(arctan(x))) (odd powers only).
• A012022 (program): Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).
• A012023 (program): Expansion of e.g.f. cos(sin(arctan(x))) (even powers).
• A012024 (program): E.g.f. sinh(sin(arctan(x))) (odd powers only).
• A012025 (program): E.g.f. arcsinh(sin(arctan(x))) = arcsinh(x/(1+x^2)^(1/2)) (odd powers only).
• A012027 (program): E.g.f. cosh(sin(arctan(x))) = cosh(x/sqrt(1+x^2)) (even powers only).
• A012125 (program): Expansion of x/ (1-4*x+16*x^2)^(3/2).
• A012132 (program): Numbers z such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x,y.
• A012150 (program): Expansion of e.g.f. exp(tan(arcsin(x))).
• A012244 (program): a(n+2) = (2n+3)*a(n+1) + (n+1)^2*a(n), a(0) = 1, a(1) = 1.
• A012245 (program): Characteristic function of factorial numbers; also decimal expansion of Liouville’s number or Liouville’s constant.
• A012249 (program): Volume of a certain rational polytope whose points with given denominator count certain sets of Standard Tableaux.
• A012250 (program): A012249(2n) divided by 2^(2n-1).
• A012393 (program): E.g.f. arctanh(tan(x)*tan(x)) (even powers only).
• A012493 (program): Take every 5th term of Padovan sequence A000931, beginning with the fifth term.
• A012509 (program): E.g.f.: -log(cos(x)*cos(x)) (even powers only).
• A012770 (program): -log(cosh(x)*cos(x))=-4/4!*x^4-544/8!*x^8-707584/12!*x^12…
• A012772 (program): Take every 5th term of Padovan sequence A000931, beginning with the sixth term.
• A012781 (program): Take every 5th term of Padovan sequence A000931, beginning with the second term.
• A012814 (program): Take every 5th term of Padovan sequence A000931, beginning with the third term.
• A012816 (program): E.g.f. arctan(sec(x)*sinh(x)) (odd powers only).
• A012853 (program): Expansion of sec(x)^2+sech(x)^2 in powers of x^4.
• A012855 (program): a(0) = 0, a(1) = 1, a(2) = 1; thereafter a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3).
• A012858 (program): Numerator of [x^(4n+2)] in the Taylor series log(cosec(x)*sinh(x))= x^2/3 +2*x^6/2835 +2*x^10/467775 +4*x^14/127702575 +..
• A012864 (program): Take every 5th term of Padovan sequence A000931, beginning with the first term.
• A012866 (program): a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
• A012870 (program): Numerator of [x^(4n+2)] in the Taylor series -log(cot(x)*tanh(x))= 2*x^2/3 +124*x^6/2835 +292*x^10/66825 +65528*x^14/127702575 -…
• A012880 (program): a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
• A012886 (program): a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
• A012899 (program): E.g.f.: exp(arcsin(x)+log(x+1)).
• A012960 (program): Expansion of e.g.f. exp(arctan(x)+log(x+1)).
• A013013 (program): exp(sinh(x)+log(x+1))=1+2*x+3/2!*x^2+5/3!*x^3+13/4!*x^4+37/5!*x^5…
• A013104 (program): sin(arcsinh(x)+arctan(x))=2*x-11/3!*x^3+185/5!*x^5-6785/7!*x^7…
• A013108 (program): cos(arcsinh(x)+arctan(x))=1-4/2!*x^2+40/4!*x^4-1030/6!*x^6+51160/8!*x^8…
• A013155 (program): Expansion of e.g.f.: exp(arctanh(x)+log(x+1))=1+2*x+3/2!*x^2+6/3!*x^3+21/4!*x^4+90/5!*x^5…
• A013170 (program): Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).
• A013174 (program): exp(arctanh(x) + arctan(x)) = 1 + 2*x + 4/2!*x^2 + 8/3!*x^3 + 16/4!*x^4 + 80/5!*x^5 +…
• A013175 (program): sin(arctanh(x)+arctan(x))=2*x-8/3!*x^3+80/5!*x^5-4160/7!*x^7…
• A013179 (program): cos(arctanh(x)+arctan(x))=1-4/2!*x^2+16/4!*x^4-640/6!*x^6+21760/8!*x^8…
• A013299 (program): -sinh(log(x+1)-arctanh(x)) = 1/2!*x^2 + 6/4!*x^4 + 135/6!*x^6 + 6300/8!*x^8 + …
• A013302 (program): E.g.f.: cosh(log(x+1)-arctanh(x)) (even powers only).
• A013304 (program): sech(log(x+1)-arctanh(x))=1-3/4!*x^4-90/6!*x^6-4095/8!*x^8…
• A013326 (program): Expansion of -(2*x^3-x^2+x-1)/(x^4-3*x^3+3*x^2-3*x+1).
• A013397 (program): exp(arcsin(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-25/5!*x^5…
• A013430 (program): Expansion of e.g.f. exp(arcsin(x)-arctanh(x)).
• A013436 (program): cosh(arcsin(x)-arctanh(x))=1+10/6!*x^6+840/8!*x^8+87750/10!*x^10…
• A013459 (program): Expansion of e.g.f. exp(arctan(x) - log(x+1)).
• A013462 (program): Expansion of e.g.f.: exp(arctan(x)-arctanh(x))=1-4/3!*x^3+160/6!*x^6-1440/7!*x^7…
• A013463 (program): E.g.f.: sin(arctan(x) - arctanh(x)) (odd powers only).
• A013465 (program): cos(arctan(x)-arctanh(x))=1-160/6!*x^6-691200/10!*x^10+3942400/12!*x^12…
• A013488 (program): Expansion of e.g.f.: exp(sinh(x)-log(x+1))=1+1/2!*x^2-1/3!*x^3+9/4!*x^4-33/5!*x^5…
• A013492 (program): exp(arcsinh(x)-log(x+1)) = 1+1/2!*x^2-3/3!*x^3+9/4!*x^4-45/5!*x^5…
• A013498 (program): Number of permutations in S_n with a certain property.
• A013499 (program): a(n) = 2*n^n, n >= 2, otherwise a(n) = 1.
• A013523 (program): Denominator of [x^(2n+1)] in the Taylor expansion arcsinh(cosec(x) - cot(x)).
• A013525 (program): E.g.f.: x + (gdinv x - sinh x)/2, where gdinv = inverse-Gudermannian. Sequence has odd-indexed coefficients; others are zero.
• A013574 (program): Minimal scope of an (n,2) difference triangle.
• A013575 (program): Minimal scope of an (n,3) difference triangle.
• A013576 (program): Minimal scope of an (n,4) difference triangle.
• A013580 (program): Triangle formed in same way as Pascal’s triangle (A007318) except 1 is added to central element in even-numbered rows.
• A013588 (program): Smallest positive integer not the determinant of an n X n {0,1}-matrix.
• A013609 (program): Triangle of coefficients in expansion of (1+2*x)^n.
• A013610 (program): Triangle of coefficients in expansion of (1+3*x)^n.
• A013611 (program): Triangle of coefficients in expansion of (1+4x)^n.
• A013612 (program): Triangle of coefficients in expansion of (1+5x)^n.
• A013613 (program): Triangle of coefficients in expansion of (1+6x)^n.
• A013614 (program): Triangle of coefficients in expansion of (1+7x)^n.
• A013615 (program): Triangle of coefficients in expansion of (1+8x)^n.
• A013616 (program): Triangle of coefficients in expansion of (1+9x)^n.
• A013617 (program): Triangle of coefficients in expansion of (1+10x)^n.
• A013618 (program): Triangle of coefficients in expansion of (1+11x)^n.
• A013619 (program): Triangle of coefficients in expansion of (1+12x)^n.
• A013620 (program): Triangle of coefficients in expansion of (2+3x)^n.
• A013621 (program): Triangle of coefficients in expansion of (2+5x)^n.
• A013622 (program): Triangle of coefficients in expansion of (3+5x)^n.
• A013623 (program): Triangle of coefficients in expansion of (2+7x)^n.
• A013624 (program): Triangle of coefficients in expansion of (3+7x)^n.
• A013625 (program): Triangle of coefficients in expansion of (4+7x)^n.
• A013626 (program): Triangle of coefficients in expansion of (5+7x)^n.
• A013627 (program): Triangle of coefficients in expansion of (6+7x)^n.
• A013628 (program): Triangle of coefficients in expansion of (4+5x)^n.
• A013632 (program): Difference between n and the next prime greater than n.
• A013633 (program): nextprime(n) - prevprime(n).
• A013634 (program): a(n) = nextprime(n) + n.
• A013635 (program): a(n) = prevprime(n) + n.
• A013636 (program): n*nextprime(n).
• A013637 (program): n*prevprime(n).
• A013638 (program): a(n) = prevprime(n)*nextprime(n).
• A013654 (program): Each term of the period of continued fraction for sqrt(n) divides n.
• A013655 (program): a(n) = F(n+1) + L(n), where F(n) and L(n) are Fibonacci and Lucas numbers, respectively.
• A013656 (program): a(n) = n*(9*n-2).
• A013661 (program): Decimal expansion of Pi^2/6 = zeta(2) = Sum_{m>=1} 1/m^2.
• A013662 (program): Decimal expansion of zeta(4).
• A013664 (program): Decimal expansion of zeta(6).
• A013697 (program): Second term in continued fraction for zeta(n).
• A013698 (program): a(n) = binomial(3*n+2, n-1).
• A013708 (program): a(n) = 3^(2n+1).
• A013709 (program): a(n) = 4^(2n+1).
• A013710 (program): a(n) = 5^(2*n + 1).
• A013711 (program): a(n) = 6^(2n+1).
• A013712 (program): a(n) = 7^(2*n + 1).
• A013713 (program): a(n) = 8^(2n+1).
• A013714 (program): a(n) = 9^(2*n + 1).
• A013715 (program): a(n) = 10^(2n+1).
• A013716 (program): a(n) = 11^(2*n + 1).
• A013717 (program): a(n) = 12^(2*n + 1).
• A013718 (program): a(n) = 13^(2*n + 1).
• A013719 (program): a(n) = 14^(2*n + 1).
• A013720 (program): a(n) = 15^(2*n + 1).
• A013721 (program): a(n) = 16^(2*n + 1).
• A013722 (program): a(n) = 17^(2*n + 1).
• A013723 (program): a(n) = 18^(2*n + 1).
• A013724 (program): a(n) = 19^(2*n + 1).
• A013725 (program): a(n) = 20^(2*n + 1).
• A013726 (program): a(n) = 21^(2*n + 1).
• A013727 (program): a(n) = 22^(2*n + 1).
• A013728 (program): a(n) = 23^(2*n + 1).
• A013729 (program): a(n) = 24^(2*n + 1).
• A013730 (program): a(n) = 2^(3n+1).
• A013731 (program): a(n) = 2^(3*n+2).
• A013732 (program): a(n) = 3^(3*n + 1).
• A013733 (program): a(n) = 3^(3n+2).
• A013734 (program): a(n) = 4^(3*n+1).
• A013735 (program): a(n) = 4^(3*n+2).
• A013736 (program): a(n) = 5^(3*n + 1).
• A013737 (program): a(n) = 5^(3*n + 2).
• A013738 (program): a(n) = 6^(3*n + 1).
• A013739 (program): a(n) = 6^(3*n + 2).
• A013740 (program): a(n) = 7^(3*n + 1).
• A013741 (program): a(n) = 7^(3*n + 2).
• A013742 (program): a(n) = 8^(3*n + 1).
• A013743 (program): a(n) = 8^(3*n + 2).
• A013744 (program): a(n) = 9^(3*n + 1).
• A013745 (program): a(n) = 9^(3*n + 2).
• A013746 (program): a(n) = 10^(3*n + 1).
• A013747 (program): a(n) = 10^(3*n + 2).
• A013748 (program): a(n) = 11^(3*n + 1).
• A013749 (program): a(n) = 11^(3*n + 2).
• A013750 (program): a(n) = 12^(3*n + 1).
• A013753 (program): a(n) = 13^(3*n + 2).
• A013754 (program): a(n) = 14^(3*n + 1).
• A013755 (program): a(n) = 14^(3*n + 2).
• A013756 (program): a(n) = 15^(3*n + 1).
• A013757 (program): a(n) = 15^(3*n + 2).
• A013758 (program): a(n) = 16^(3n+1).
• A013761 (program): a(n) = 17^(3*n + 2).
• A013766 (program): 20^(3n+1).
• A013767 (program): a(n) = 20^(3*n + 2).
• A013768 (program): a(n) = 21^(3*n + 1).
• A013769 (program): a(n) = 21^(3*n + 2).
• A013770 (program): a(n) = 22^(3*n + 1).
• A013771 (program): a(n) = 22^(3*n + 2).
• A013772 (program): a(n) = 23^(3*n + 1).
• A013776 (program): a(n) = 2^(4*n+1).
• A013777 (program): a(n) = 2^(4*n + 3).
• A013778 (program): a(n) = 3^(4*n + 1).
• A013779 (program): a(n) = 3^(4*n + 3).
• A013780 (program): a(n) = 4^(4*n + 1).
• A013781 (program): a(n) = 4^(4*n + 3).
• A013782 (program): a(n) = 5^(4*n + 1).
• A013783 (program): a(n) = 5^(4*n + 3).
• A013784 (program): a(n) = 6^(4*n + 1).
• A013785 (program): a(n) = 6^(4n+3).
• A013786 (program): a(n) = 7^(4*n + 1).
• A013787 (program): a(n) = 7^(4*n + 3).
• A013788 (program): a(n) = 8^(4*n + 1).
• A013789 (program): a(n) = 8^(4*n + 3).
• A013790 (program): a(n) = 9^(4*n + 1).
• A013791 (program): a(n) = 9^(4*n + 3).
• A013792 (program): a(n) = 10^(4*n + 1).
• A013794 (program): a(n) = 11^(4n+1).
• A013796 (program): a(n) = 12^(4*n + 1).
• A013822 (program): a(n) = 2^(5*n + 1).
• A013823 (program): a(n) = 2^(5*n + 2).
• A013824 (program): a(n) = 2^(5*n + 3).
• A013825 (program): a(n) = 2^(5*n + 4).
• A013826 (program): a(n) = 3^(5*n + 1).
• A013827 (program): a(n) = 3^(5*n + 2).
• A013828 (program): a(n) = 3^(5*n + 3).
• A013829 (program): a(n) = 3^(5*n + 4).
• A013830 (program): a(n) = 4^(5*n + 1).
• A013831 (program): a(n) = 4^(5n+2).
• A013832 (program): a(n) = 4^(5*n + 3).
• A013833 (program): a(n) = 4^(5*n + 4).
• A013834 (program): a(n) = 5^(5*n + 1).
• A013835 (program): a(n) = 5^(5*n + 2).
• A013836 (program): a(n) = 5^(5*n + 3).
• A013837 (program): a(n) = 5^(5*n + 4).
• A013838 (program): a(n) = 6^(5*n + 1).
• A013839 (program): a(n) = 6^(5n+2).
• A013840 (program): a(n) = 6^(5*n + 3).
• A013841 (program): a(n) = 6^(5*n + 4).
• A013842 (program): a(n) = 7^(5*n + 1).
• A013843 (program): a(n) = 7^(5*n + 2).
• A013915 (program): a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.
• A013919 (program): Numbers n such that sum of first n composites is composite.
• A013920 (program): Composite numbers k such that the sum of all composites <= k is composite.
• A013921 (program): Composite numbers that are equal to the sum of the first k composites for some k.
• A013926 (program): a(n) = (2*n)! * D_{2*n}, where D_{2*n} = (1/Pi) * Integral_{x=0..oo} [1 - x^(2*n) / Product_{j=1..n} (x^2+j^2)] dx.
• A013928 (program): Number of (positive) squarefree numbers < n.
• A013929 (program): Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.
• A013936 (program): a(n) = Sum_{k=1..n} floor(n/k^2).
• A013937 (program): a(n) = Sum_{k=1..n} floor(n/k^3).
• A013938 (program): a(n) = Sum_{k=1..n} floor(n/k^4).
• A013939 (program): Partial sums of sequence A001221 (number of distinct primes dividing n).
• A013940 (program): a(n) = Sum_{k=1..n} floor(n/prime(k)^2).
• A013941 (program): a(n) = Sum_{k = 1..n} floor(n/prime(k)^3).
• A013942 (program): Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.
• A013945 (program): Least d such that period of continued fraction for sqrt(d) contains n (n^2+2 if n odd, (n/2)^2+1 if n even).
• A013946 (program): Least d for which the number with continued fraction [n,n,n,n…] is in Q(sqrt(d)).
• A013947 (program): Positions of 1’s in Kolakoski sequence (A000002).
• A013948 (program): Positions of 2’s in Kolakoski sequence (A000002).
• A013954 (program): a(n) = sigma_6(n), the sum of the 6th powers of the divisors of n.
• A013955 (program): a(n) = sigma_7(n), the sum of the 7th powers of the divisors of n.
• A013956 (program): sigma_8(n), the sum of the 8th powers of the divisors of n.
• A013957 (program): sigma_9(n), the sum of the 9th powers of the divisors of n.
• A013958 (program): a(n) = sigma_10(n), the sum of the 10th powers of the divisors of n.
• A013959 (program): a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.
• A013960 (program): a(n) = sigma_12(n), the sum of the 12th powers of the divisors of n.
• A013961 (program): a(n) = sigma_13(n), the sum of the 13th powers of the divisors of n.
• A013962 (program): a(n) = sigma_14(n), the sum of the 14th powers of the divisors of n.
• A013963 (program): a(n) = sigma_15(n), the sum of the 15th powers of the divisors of n.
• A013964 (program): a(n) = sigma_16(n), the sum of the 16th powers of the divisors of n.
• A013965 (program): a(n) = sigma_17(n), the sum of the 17th powers of the divisors of n.
• A013966 (program): a(n) = sigma_18(n), the sum of the 18th powers of the divisors of n.
• A013967 (program): a(n) = sigma_19(n), the sum of the 19th powers of the divisors of n.
• A013968 (program): a(n) = sigma_20(n), the sum of the 20th powers of the divisors of n.
• A013969 (program): a(n) = sigma_21(n), the sum of the 21st powers of the divisors of n.
• A013970 (program): a(n) = sum of 22nd powers of divisors of n.
• A013971 (program): a(n) = sum of 23rd powers of divisors of n.
• A013972 (program): a(n) = sum of 24th powers of divisors of n.
• A013973 (program): Expansion of Eisenstein series E_6(q) (alternate convention E_3(q)).
• A013974 (program): Eisenstein series E_10(q) (alternate convention E_5(q)).
• A013979 (program): Expansion of 1/(1 - x^2 - x^3 - x^4) = 1/((1 + x)*(1 - x - x^3)).
• A013981 (program): Number of commutative elements in Coxeter group H_n.
• A013982 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5).
• A013983 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6).
• A013984 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7).
• A013985 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8).
• A013986 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
• A013987 (program): Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10).
• A013989 (program): a(n) = (n+1)*(a(n-1)/n + a(n-2)), with a(0)=1, a(1)=2.
• A013999 (program): From applying the “rational mean” to the number e.
• A014001 (program): Pisot sequence E(7,15), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
• A014002 (program): Pisot sequence E(8,14), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
• A014003 (program): Pisot sequence E(9,15), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A014004 (program): Pisot sequence E(9,17), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
• A014005 (program): Pisot sequence E(9,19), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
• A014006 (program): Pisot sequence E(10,18), a(n)=[ a(n-1)^2/a(n-2)+1/2 ].
• A014007 (program): Pisot sequence E(10,21), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
• A014008 (program): Pisot sequence E(10,22), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
• A014009 (program): First differences of Shallit sequence S(3,7) (A020730).
• A014010 (program): Linear recursion relative of Shallit sequence S(2,6).
• A014016 (program): Expansion of inverse of 7th cyclotomic polynomial; period 7: repeat [1, -1, 0, 0, 0, 0, 0].
• A014017 (program): Inverse of 8th cyclotomic polynomial.
• A014018 (program): Inverse of 9th cyclotomic polynomial.
• A014019 (program): Inverse of 10th cyclotomic polynomial.
• A014020 (program): Inverse of 11th cyclotomic polynomial.
• A014021 (program): Inverse of 12th cyclotomic polynomial.
• A014022 (program): Inverse of 13th cyclotomic polynomial.
• A014023 (program): Inverse of 14th cyclotomic polynomial.
• A014024 (program): Inverse of 15th cyclotomic polynomial.
• A014025 (program): Expansion of the inverse of the 16th cyclotomic polynomial.
• A014026 (program): Inverse of 17th cyclotomic polynomial.
• A014027 (program): Inverse of 18th cyclotomic polynomial.
• A014028 (program): Inverse of 19th cyclotomic polynomial.
• A014029 (program): Inverse of 20th cyclotomic polynomial.
• A014030 (program): Inverse of 21st cyclotomic polynomial.
• A014031 (program): Inverse of 22nd cyclotomic polynomial.
• A014032 (program): Inverse of 23rd cyclotomic polynomial.
• A014033 (program): Inverse of 24th cyclotomic polynomial.
• A014034 (program): Inverse of 25th cyclotomic polynomial.
• A014035 (program): Inverse of 26th cyclotomic polynomial.
• A014036 (program): Inverse of 27th cyclotomic polynomial.
• A014037 (program): Inverse of 28th cyclotomic polynomial.
• A014038 (program): Inverse of 29th cyclotomic polynomial.
• A014039 (program): Inverse of 30th cyclotomic polynomial.
• A014040 (program): Inverse of 31st cyclotomic polynomial.
• A014041 (program): Inverse of 32nd cyclotomic polynomial.
• A014043 (program): Inverse of 34th cyclotomic polynomial.
• A014045 (program): Inverse of 36th cyclotomic polynomial.
• A014047 (program): Inverse of 38th cyclotomic polynomial.
• A014049 (program): Inverse of 40th cyclotomic polynomial.
• A014050 (program): a(n) = (n^2+1)^n.
• A014051 (program): Inverse of 42nd cyclotomic polynomial.
• A014052 (program): a(n) = floor((n+1/n)^n).
• A014053 (program): Inverse of 44th cyclotomic polynomial.
• A014054 (program): Inverse of 45th cyclotomic polynomial.
• A014055 (program): Inverse of 46th cyclotomic polynomial.
• A014056 (program): Nearest integer to (n + 1/n)^n.
• A014057 (program): Inverse of 48th cyclotomic polynomial.
• A014058 (program): a(n) = ceiling((n+1/n)^n).
• A014059 (program): Inverse of 50th cyclotomic polynomial.
• A014061 (program): Inverse of 52nd cyclotomic polynomial.
• A014062 (program): a(n) = binomial(n^2, n).
• A014063 (program): Inverse of 54th cyclotomic polynomial.
• A014065 (program): Inverse of 56th cyclotomic polynomial.
• A014067 (program): Inverse of 58th cyclotomic polynomial.
• A014068 (program): a(n) = binomial(n*(n+1)/2, n).
• A014069 (program): Inverse of 60th cyclotomic polynomial.
• A014070 (program): a(n) = binomial(2^n, n).
• A014071 (program): Inverse of 62nd cyclotomic polynomial.
• A014072 (program): Inverse of 63rd cyclotomic polynomial.
• A014076 (program): Odd nonprimes.
• A014081 (program): a(n) is the number of occurrences of ‘11’ in binary expansion of n.
• A014082 (program): Number of occurrences of ‘111’ in binary expansion of n.
• A014084 (program): Inverse of 75th cyclotomic polynomial.
• A014085 (program): Number of primes between n^2 and (n+1)^2.
• A014089 (program): Sum of a square and a prime.
• A014091 (program): Numbers that are the sum of 2 primes.
• A014092 (program): Numbers that are not the sum of 2 primes.
• A014093 (program): Inverse of 84th cyclotomic polynomial.
• A014097 (program): a(n) = a(n-1)+a(n-4).
• A014098 (program): a(n)=a(n-1)+a(n-4).
• A014099 (program): Inverse of 90th cyclotomic polynomial.
• A014101 (program): a(n) = a(n-1) + a(n-4), starting 1,1,1,3.
• A014103 (program): Expansion of (eta(q^2) / eta(q))^24 in powers of q.
• A014105 (program): Second hexagonal numbers: a(n) = n*(2*n + 1).
• A014106 (program): a(n) = n*(2*n + 3).
• A014107 (program): a(n) = n*(2*n-3).
• A014109 (program): Number of possible circular rhymes of n strophes.
• A014110 (program): Number of ordered ways of writing n as a sum of 4 squares of natural numbers.
• A014112 (program): a(n) = n*(n-1) + (n-2)*(n-3) + … + 1*0 + 1 for n odd; otherwise, a(n) = n*(n-1) + (n-2)*(n-3) + … + 2*1.
• A014113 (program): a(n) = a(n-1) + 2*a(n-2) with a(0)=0, a(1)=2.
• A014118 (program): Write in binary and read in ternary!.
• A014125 (program): Bisection of A001400.
• A014126 (program): Number of partitions of 2*n into at most 4 parts.
• A014129 (program): Inverse of 120th cyclotomic polynomial.
• A014130 (program): ((n+3)!/6)*product( 2*k+1, k=0..n).
• A014131 (program): a(n) = 2*a(n-1) if n odd else 2*a(n-1) + 6.
• A014132 (program): Complement of triangular numbers (A000217); also array T(n,k) = ((n+k)^2 + n-k)/2, n, k > 0, read by antidiagonals.
• A014133 (program): Sum of a square and a triangular number.
• A014134 (program): Numbers that are not the sum of a square (A000290) and a triangular number (A000217).
• A014135 (program): Inverse of 126th cyclotomic polynomial.
• A014137 (program): Partial sums of Catalan numbers (A000108).
• A014138 (program): Partial sums of (Catalan numbers starting 1, 2, 5, …).
• A014140 (program): Apply partial sum operator twice to Catalan numbers.
• A014143 (program): Partial sums of A014138.
• A014144 (program): Apply partial sum operator twice to factorials.
• A014145 (program): Partial sums of A007489.
• A014146 (program): Partial sums of A003136.
• A014148 (program): a(n) = Sum_{m=1..n} Sum_{k=1..m} prime(k).
• A014150 (program): Apply partial sum operator thrice to primes.
• A014151 (program): Apply partial sum operator thrice to Catalan numbers.
• A014153 (program): Expansion of 1/((1-x)^2*Product_{k>=1} (1-x^k)).
• A014155 (program): Sum of a nonnegative cube and a triangular number.
• A014156 (program): Numbers that are not the sum of a nonnegative cube and a triangular number.
• A014159 (program): Inverse of 150th cyclotomic polynomial.
• A014160 (program): Apply partial sum operator thrice to partition numbers.
• A014161 (program): Apply partial sum operator 4 times to partition numbers.
• A014162 (program): Apply partial sum operator thrice to Fibonacci numbers.
• A014166 (program): Apply partial sum operator 4 times to Fibonacci numbers.
• A014176 (program): Decimal expansion of the silver mean, 1+sqrt(2).
• A014177 (program): Inverse of 168th cyclotomic polynomial.
• A014178 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^3*binomial(n+k,k).
• A014180 (program): Sum_{k = 0..n} binomial(n,k)^3*binomial(n+k,k)^2.
• A014181 (program): Numbers > 9 with all digits the same.
• A014182 (program): Expansion of e.g.f. exp(1-x-exp(-x)).
• A014186 (program): Squares of palindromes.
• A014187 (program): Cubes of palindromes.
• A014188 (program): Fourth powers of palindromes.
• A014189 (program): Inverse of 180th cyclotomic polynomial.
• A014190 (program): Palindromes in base 3 (written in base 10).
• A014192 (program): Palindromes in base 4 (written in base 10).
• A014193 (program): n-th prime + mu(n).
• A014198 (program): Number of integer solutions to x^2 + y^2 <= n excluding (0,0).
• A014200 (program): Number of solutions to x^2 + y^2 <= n, excluding (0,0), divided by 4.
• A014201 (program): Number of solutions to x^2+x*y+y^2 <= n excluding (0,0).
• A014202 (program): Number of solutions to x^2 + x*y + y^2 <= n, excluding (0,0), divided by 6.
• A014203 (program): Sum {i^2+j^2+k^2}, i^2+j^2+k^2 <= n.
• A014205 (program): (1/12)*(n+5)*(n+1)*n^2.
• A014206 (program): a(n) = n^2 + n + 2.
• A014208 (program): Next prime after n-th Fibonacci number.
• A014209 (program): a(n) = n^2 + 3*n - 1.
• A014213 (program): Floor((e/2)^n).
• A014215 (program): [ sqrt(3/2)^n ].
• A014217 (program): a(n) = floor(phi^n), where phi = (1+sqrt(5))/2 is the golden ratio.
• A014220 (program): Next prime after n^3.
• A014228 (program): Product of 3 successive Catalan numbers.
• A014231 (program): (Product of 3 successive Catalan numbers)/2.
• A014235 (program): Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 1 0 ].
• A014236 (program): Expansion of g.f.: 2*x*(1-x)/((1-2*x)*(1-2*x^2)).
• A014237 (program): a(n) = (n-th prime) - (n-th nonprime).
• A014238 (program): a(n) = (n-th number that is 1 or prime) - (n-th composite number).
• A014241 (program): a(n) = ((n+1)-st Fibonacci number) - (n-th non-Fibonacci number).
• A014242 (program): (n-th Fibonacci number that is not 1) - (n-th number that is 1 or not a Fibonacci number).
• A014243 (program): a(n) = ((n+1)-st Lucas number) - (n-th non-Lucas number).
• A014244 (program): (n-th Lucas number that is not 1) - (n-th number that is 1 or not a Lucas number).
• A014245 (program): a(n) = (n-th term of Beatty sequence for (3+sqrt(3))/2) - (n-th term of Beatty sequence for sqrt(3)).
• A014252 (program): a(n) = b(n) - c(n) where b(n) is the n-th Lucas number greater than 3 and c(n) is the n-th number not in sequence b( ).
• A014253 (program): a(n) = b(n)^2, where b(n) = b(n-1)^2 + b(n-2)^2 (A000283).
• A014255 (program): Expansion of (1+2*x+3*x^2)/((1-x)*(1-x^2)^2).
• A014257 (program): Product of digits of 2^n.
• A014258 (program): Iccanobif numbers: add previous two terms and reverse the sum.
• A014259 (program): Iccanobif numbers: add reversal of a(n-1) to a(n-2).
• A014260 (program): Iccanobif numbers: add a(n-1) to reversal of a(n-2).
• A014261 (program): Numbers that contain odd digits only.
• A014263 (program): Numbers that contain even digits only.
• A014283 (program): a(n) = Fibonacci(n) - n^2.
• A014284 (program): Partial sums of primes, if 1 is regarded as a prime (as it was until quite recently, see A008578).
• A014285 (program): a(n) = Sum_{j=1..n} j*prime(j).
• A014286 (program): a(n) = Sum_{j=0..n} j*Fibonacci(j).
• A014288 (program): a(n) = floor(Sum_{k=0..n} k!/2), or floor( A003422(n+1)/2 ).
• A014291 (program): Imaginary Rabbits: imaginary part of a(0)=i; a(1)=-i; a(n) = a(n-1) + i*a(n-2), with i = sqrt(-1).
• A014292 (program): a(n) = 2*a(n-1) - a(n-2) - a(n-4) with a(0) = a(1) = 0, a(2) = 1, a(3) = 2.
• A014293 (program): a(n) = n^(n+1)-n+1.
• A014297 (program): a(n) = n! * C(n+2, 2) * 2^(n+1).
• A014298 (program): a(n) = 2^n * (3n)! / (2n+1)!.
• A014300 (program): Number of nodes of odd outdegree in all ordered rooted (planar) trees with n edges.
• A014301 (program): Number of internal nodes of even outdegree in all ordered rooted trees with n edges.
• A014302 (program): a(n) = prime(n)*(prime(n-1)-1)/2.
• A014303 (program): a(n) = prime(n)*(prime(n+1)-1)/2.
• A014304 (program): Expansion of e.g.f. 1/sqrt(exp(x)*(2-exp(x))).
• A014306 (program): a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.
• A014307 (program): Expansion of the e.g.f. sqrt(exp(x) / (2 - exp(x))).
• A014309 (program): a(n) = (n+2)*(n+1)*(n^2 + 7*n - 12)/24.
• A014311 (program): Numbers with exactly 3 ones in binary expansion.
• A014312 (program): Numbers with exactly 4 ones in binary expansion.
• A014313 (program): Numbers with exactly 5 ones in binary expansion.
• A014314 (program): Number of up steps in all length n left factors of Dyck paths.
• A014316 (program): Convolution of Catalan numbers and squares.
• A014317 (program): Inverse of 308th cyclotomic polynomial.
• A014318 (program): Convolution of Catalan numbers and powers of 2.
• A014334 (program): Exponential convolution of Fibonacci numbers with themselves.
• A014335 (program): Exponential convolution of Fibonacci numbers with themselves (divided by 2).
• A014336 (program): Three-fold exponential convolution of Fibonacci numbers with themselves.
• A014337 (program): Three-fold exponential convolution of Fibonacci numbers with themselves (divided by 6).
• A014368 (program): a(n) = bc, where n = C(b,2)+C(c,1), b>c>=0.
• A014369 (program): a(n) = bcd, where n = C(b,3)+C(c,2)+C(d,1), b>c>d>=0.
• A014370 (program): If n = binomial(b,2)+binomial(c,1), b>c>=0 then a(n) = binomial(b+1,3)+binomial(c+1,2).
• A014373 (program): Inverse of 364th cyclotomic polynomial.
• A014390 (program): Final 2 digits of 7^n.
• A014391 (program): Final digit of 8^n.
• A014392 (program): Final 2 digits of 8^n.
• A014393 (program): Final 2 digits of 9^n.
• A014401 (program): Denominators of coefficients of expansion of Bessel function J_3(x).
• A014402 (program): Numbers found in denominators of expansion of Airy function Ai(x).
• A014403 (program): Numbers found in denominators of expansion of Airy function Bi(x).
• A014409 (program): Number of inequivalent ways (mod D_4) a pair of checkers can be placed on an n X n board.
• A014410 (program): Elements in Pascal’s triangle (by row) that are not 1.
• A014411 (program): Triangular array formed from elements to right of middle of rows of Pascal’s triangle that are not 1.
• A014413 (program): Triangular array formed from elements to right of middle of Pascal’s triangle.
• A014414 (program): Odd elements in Pascal’s triangle that are not 1.
• A014417 (program): Representation of n in base of Fibonacci numbers (the Zeckendorf representation of n). Also, binary words starting with 1 not containing 11, with the word 0 added.
• A014419 (program): Write n in base of Catalan numbers, then interpret as if written in base 3.
• A014421 (program): Odd elements in Pascal’s triangle.
• A014428 (program): Even elements in Pascal’s triangle.
• A014430 (program): Subtract 1 from Pascal’s triangle, read by rows.
• A014431 (program): a(1) = 1, a(2) = 2, a(n) = a(1)*a(n-1) + a(2)*a(n-2) + …+ a(n-2)*a(2) for n >= 3.
• A014432 (program): a(n) = Sum_{i=1..n-1} a(i)*a(n-1-i), with a(0) = 1, a(1) = 3.
• A014433 (program): a(n) = sum(i=0..n-1, a(i)*a(n-i) ), a(0) = 1, a(1)=4.
• A014434 (program): Sum[ a[ i ]a[ n-i ],{i,0,n-1} ], a[ 0 ] == 1, a[ 1 ]==5.
• A014435 (program): Sum( a(i)*a(n-i), i=0..n-1 ), with a(0)=1, a(1)=6.
• A014436 (program): Inverse of 427th cyclotomic polynomial.
• A014437 (program): Odd Fibonacci numbers.
• A014442 (program): Largest prime factor of n^2 + 1.
• A014445 (program): Even Fibonacci numbers; or, Fibonacci(3*n).
• A014447 (program): Odd Lucas numbers.
• A014448 (program): Even Lucas numbers: L(3n).
• A014449 (program): Numbers in the triangle of Eulerian numbers (A008292) that are not 1.
• A014450 (program): Even numbers in the triangle of Eulerian numbers.
• A014455 (program): Theta series of quadratic form with Gram matrix [ 1, 0, 0; 0, 1, 0; 0, 0, 2 ]. Number of integer solutions to x^2 + y^2 + 2*z^2 = n.
• A014459 (program): Odd numbers in the triangle of Eulerian numbers.
• A014461 (program): Odd numbers in the triangle of Eulerian numbers that are not 1.
• A014462 (program): Triangular array formed from elements to left of middle of Pascal’s triangle.
• A014463 (program): Triangular array formed from elements to left of middle of rows of Pascal’s triangle that are not 1.
• A014465 (program): A063691 without zeros.
• A014473 (program): Pascal’s triangle - 1.
• A014475 (program): Triangular array formed from odd elements to right of middle of rows of Pascal’s triangle.
• A014476 (program): Triangular array formed from even elements to right of middle of rows of Pascal’s triangle.
• A014477 (program): Expansion of (1 + 2*x)/(1 - 2*x)^3.
• A014479 (program): Exponential generating function = (1+2*x)/(1-2*x)^3.
• A014480 (program): Expansion of (1+2*x)/(1-2*x)^2.
• A014481 (program): a(n) = 2^n*n!*(2*n+1).
• A014483 (program): Expansion of (1+2*x) / (1-2*x)^4.
• A014484 (program): Expansion of (1+2x)/(1-2x)^4 (E.g.f.).
• A014485 (program): Inverse of 476th cyclotomic polynomial.
• A014486 (program): List of totally balanced sequences of 2n binary digits written in base 10. Binary expansion of each term contains n 0’s and n 1’s and reading from left to right (the most significant to the least significant bit), the number of 0’s never exceeds the number of 1’s.
• A014491 (program): a(n) = gcd(n, 2^n - 1).
• A014493 (program): Odd triangular numbers.
• A014494 (program): Even triangular numbers.
• A014495 (program): Central binomial coefficient - 1.
• A014499 (program): Number of 1’s in binary representation of n-th prime.
• A014506 (program): Inverse of 497th cyclotomic polynomial.
• A014508 (program): a(n) = floor( n! / e ).
• A014509 (program): Truncation of Bernoulli number: floor(|B_2n|) * sign(B_2n).
• A014523 (program): Number of Hamiltonian paths in a 4 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.
• A014524 (program): Number of Hamiltonian paths from NW to SW corners in a grid with 2n rows and 4 columns.
• A014528 (program): Neither == 0 (mod 4) nor a power of 3.
• A014531 (program): Form array in which n-th row is obtained by expanding (1+x+x^2)^n and taking the 2nd column from the center.
• A014532 (program): Form array in which n-th row is obtained by expanding (1+x+x^2)^n and taking the 3rd column from the center.
• A014533 (program): Form array in which n-th row is obtained by expanding (1 + x + x^2)^n and taking the 4th column from the center.
• A014541 (program): Inverse of 532nd cyclotomic polynomial.
• A014549 (program): Decimal expansion of 1 / M(1,sqrt(2)) (Gauss’s constant).
• A014550 (program): Binary reflected Gray code.
• A014551 (program): Jacobsthal-Lucas numbers.
• A014553 (program): Maximal multiplicative persistence (or length) of any n-digit number.
• A014557 (program): Multiplicity of K_3 in K_n.
• A014566 (program): Sierpiński numbers of the first kind: n^n + 1.
• A014567 (program): Numbers k such that k and sigma(k) are relatively prime, where sigma(k) = sum of divisors of k (A000203).
• A014571 (program): Consider the Morse-Thue sequence (A010060) as defining a binary constant and convert it to decimal.
• A014574 (program): Average of twin prime pairs.
• A014577 (program): The regular paper-folding sequence (or dragon curve sequence).
• A014578 (program): Binary expansion of Thue constant (or Roth’s constant).
• A014591 (program): a(n) = floor(n^2/12 + 5/4).
• A014601 (program): Numbers congruent to 0 or 3 mod 4.
• A014605 (program): Partial sums of A001935; at one time this was conjectured to agree with A007478.
• A014606 (program): a(n) = (3n)!/(6^n).
• A014608 (program): a(n) = (4n)!/(24^n).
• A014609 (program): a(n) = (5n)!/(5!^n).
• A014610 (program): Tetranacci numbers arising in connection with current algebras sp(2)_n.
• A014612 (program): Numbers that are the product of exactly three (not necessarily distinct) primes.
• A014613 (program): Numbers that are products of 4 primes.
• A014614 (program): Numbers that are products of 5 primes (or 5-almost primes, a generalization of semiprimes).
• A014616 (program): a(n) = solution to the postage stamp problem with 2 denominations and n stamps.
• A014619 (program): Exponential generating function is -f(x) * int(exp(exp(-t)-1),t,0,x) where f(x) = exp(1-x-exp(-x)) is an exponential generating function for A014182.
• A014625 (program): Inverse of 616th cyclotomic polynomial.
• A014626 (program): Number of intersection points of diagonals of an n-gon in general position, plus number of vertices.
• A014628 (program): Number of segments (and sides) created by diagonals of an n-gon in general position.
• A014629 (program): Number of segments created by diagonals of n-gon.
• A014632 (program): Odd pentagonal numbers.
• A014633 (program): Even pentagonal numbers.
• A014634 (program): a(n) = (2*n+1)*(4*n+1).
• A014635 (program): a(n) = 2*n*(4*n - 1).
• A014637 (program): Odd heptagonal numbers (A000566).
• A014640 (program): Even heptagonal numbers (A000566).
• A014641 (program): Odd octagonal numbers: (2n+1)*(6n+1).
• A014642 (program): Even octagonal numbers: a(n) = 4*n*(3*n-1).
• A014653 (program): Inverse of 644th cyclotomic polynomial.
• A014657 (program): Numbers m that divide 2^k + 1 for some nonnegative k.
• A014659 (program): Odd numbers that do not divide 2^k + 1 for any k >= 1.
• A014661 (program): Numbers that do not divide 2^k + 1 for any k>0.
• A014664 (program): Order of 2 modulo the n-th prime.
• A014668 (program): a(1) = 1, a(n) = Sum_{k=1..n-1} Sum_{d|k} a(d).
• A014673 (program): Smallest prime factor of greatest proper divisor of n.
• A014675 (program): The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit).
• A014677 (program): First differences of A001468.
• A014679 (program): G.f.: (1+x^3)^2/((1-x^2)*(1-x^3)*(1-x^4)).
• A014681 (program): Fix 0; exchange even and odd numbers.
• A014682 (program): The Collatz or 3x+1 function: a(n) = n/2 if n is even, otherwise (3n+1)/2.
• A014683 (program): In the sequence of positive integers add 1 to each prime number.
• A014684 (program): In the sequence of positive integers subtract 1 from each prime number.
• A014685 (program): In sequence of positive integers add 1 to first prime and subtract 1 from 2nd prime; add 1 to 3rd prime and subtract 1 from 4th prime and so on.
• A014686 (program): In sequence of prime numbers add 1 to first prime, 3rd prime, fifth prime, … then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.
• A014687 (program): In sequence of odd primes add 1 to first prime, 3rd prime, 5th prime, … then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.
• A014688 (program): a(n) = n-th prime + n.
• A014689 (program): a(n) = prime(n)-n, the number of nonprimes less than prime(n).
• A014690 (program): a(n) = n + prime(n+1).
• A014692 (program): a(n) = prime(n) - (n-1).
• A014693 (program): In sequence of prime numbers add 1 to first number, 2 to 3rd number, 3 to 5th number, … then subtract 1 from 2nd number, 2 from 4th number, 3 from 6th number and so on.
• A014694 (program): a(n) = prime(n+1) - (-1)^n*ceiling(n/2).
• A014695 (program): Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of Q_8.
• A014701 (program): Number of multiplications to compute n-th power by the Chandah-sutra method.
• A014705 (program): Expansion of ((theta_2)^4 + (theta_3)^4) / eta(z/2)^4.
• A014707 (program): a(4n) = 0, a(4n+2) = 1, a(2n+1) = a(n).
• A014709 (program): The regular paper-folding (or dragon curve) sequence.
• A014710 (program): The regular paper-folding (or dragon curve) sequence.
• A014717 (program): a(n) = (F(n+1) + L(n))^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032).
• A014718 (program): a(n) = (F(n+1)+L(n)+n)^2 where F(n) are the Fibonacci numbers (A000045) and L(n) are the Lucas numbers (A000032).
• A014719 (program): Squares of elements in Pascal triangle (by row) that are not 1.
• A014720 (program): Squares of elements to right of central element in Pascal triangle (by row) that are not 1.
• A014721 (program): Squares of elements to left of the central element in Pascal triangle (by row).
• A014725 (program): Squares of odd elements in Pascal triangle that are not 1.
• A014726 (program): Squares of odd elements in Pascal triangle.
• A014727 (program): Squares of even elements in Pascal’s triangle A007318.
• A014728 (program): Squares of odd Fibonacci numbers.
• A014729 (program): Squares of even Fibonacci numbers.
• A014730 (program): Squares of odd Lucas numbers.
• A014731 (program): Squares of even Lucas numbers.
• A014732 (program): Squares of numbers in triangle of Eulerian numbers that are not 1.
• A014733 (program): Squares of even numbers in triangle of Eulerian numbers.
• A014734 (program): Squares of odd numbers in triangle of Eulerian numbers.
• A014735 (program): Squares of odd numbers in triangle of Eulerian numbers that are not 1.
• A014736 (program): Squares of odd triangular numbers.
• A014737 (program): Inverse of 728th cyclotomic polynomial.
• A014738 (program): Squares of even triangular numbers.
• A014739 (program): Expansion of (1+x^2)/(1-2*x+x^3).
• A014742 (program): Expansion of (1+x^2)/(1 - 2*x - 2*x^2 + x^3).
• A014743 (program): Expansion of (1+x)/(1-x-x^2-x^4-x^5).
• A014751 (program): Inverse of 742nd cyclotomic polynomial.
• A014760 (program): Squares of numbers in array formed from odd elements to the right of middle of rows of Pascal triangle that are not 1.
• A014761 (program): Squares of numbers in array formed from odd elements to the right of middle of rows of Pascal triangle.
• A014762 (program): Squares of numbers in array formed from even elements to the right of middle of rows of Pascal triangle.
• A014766 (program): Numbers k such that the 3k shuffle group does not accomplish a perfect shuffle.
• A014769 (program): Squares of odd pentagonal numbers.
• A014770 (program): Squares of even pentagonal numbers.
• A014771 (program): Squares of odd hexagonal numbers.
• A014772 (program): Squares of even hexagonal numbers.
• A014773 (program): Squares of odd heptagonal numbers.
• A014775 (program): Expansion of exp ( - x - (1/2)*x^2 - (1/6)*x^3).
• A014785 (program): a(n) = Sum_{0<=k<=n} ceiling(k^2/n).
• A014787 (program): Expansion of Jacobi theta constant (theta_2/2)^12.
• A014792 (program): Squares of even heptagonal numbers.
• A014793 (program): Squares of odd octagonal numbers.
• A014794 (program): Squares of even octagonal numbers.
• A014795 (program): Squares of odd tetrahedral numbers.
• A014796 (program): Squares of even tetrahedral numbers (A015220).
• A014797 (program): Squares of odd square pyramidal numbers.
• A014798 (program): Squares of even square pyramidal numbers.
• A014799 (program): Squares of odd pentagonal pyramidal numbers.
• A014800 (program): Squares of even pentagonal pyramidal numbers.
• A014801 (program): Squares of odd hexagonal pyramidal numbers.
• A014803 (program): Squares of even hexagonal pyramidal numbers.
• A014805 (program): Expansion of Jacobi theta constant (theta_2/2)^16.
• A014809 (program): Expansion of Jacobi theta constant (theta_2/2)^24.
• A014811 (program): a(n) = Sum_{k=1..n-1} ceiling(k^2/n).
• A014813 (program): a(n) = Sum_{k=0..n} ceiling(k^3/n).
• A014816 (program): a(n) = Sum_{k=1..n} ceiling(k^4/n).
• A014817 (program): a(n) = Sum_{k=1..n} floor(k^2/n).
• A014818 (program): a(n) is the sum over all floor(k^3/n), k=0 to n inclusive.
• A014819 (program): a(n) = Sum_{k=1..n} floor(k^4/n).
• A014820 (program): a(n) = (1/3)*(n^2 + 2*n + 3)*(n+1)^2.
• A014821 (program): Inverse of 812th cyclotomic polynomial.
• A014822 (program): Numbers k such that k divides s(k), where s(1)=1, s(j)=10*s(j-1)+j (A014824).
• A014824 (program): a(0) = 0; for n>0, a(n) = 10*a(n-1) + n.
• A014825 (program): a(n) = 4*a(n-1) + n with n > 1, a(1)=1.
• A014827 (program): a(1)=1, a(n) = 5*a(n-1) + n.
• A014829 (program): a(1)=1, a(n) = 6*a(n-1) + n.
• A014830 (program): a(1)=1; for n > 1, a(n) = 7*a(n-1) + n.
• A014831 (program): a(1)=1; for n>1, a(n) = 8*a(n-1)+n.
• A014832 (program): a(1)=1; for n>1, a(n) = 9*a(n-1)+n.
• A014833 (program): a(n) = 2^n - n(n+1)/2.
• A014835 (program): Inverse of 826th cyclotomic polynomial.
• A014836 (program): Sum modulo n of all the digits of n in every base from 2 to n-1.
• A014837 (program): Sum of all the digits of n in every base from 2 to n-1.
• A014844 (program): a(n) = 2^n - n*(n-1)/2.
• A014846 (program): 2^(n-1) - n*(n+1)/2.
• A014847 (program): Numbers k such that k-th Catalan number C(2k,k)/(k+1) is divisible by k.
• A014848 (program): n^2 - floor( n/2 ).
• A014851 (program): Numbers k that divide s(k), where s(1)=1, s(j)=4*s(j-1)+j.
• A014855 (program): Numbers k that divide s(k), where s(1)=1, s(j)=8*s(j-1)+j.
• A014863 (program): Inverse of 854th cyclotomic polynomial.
• A014866 (program): Numbers k that divide s(k), where s(1)=1, s(j)=16*s(j-1)+j.
• A014871 (program): Numbers k that divide s(k), where s(1)=1, s(j)=20*s(j-1)+j.
• A014873 (program): Numbers k that divide s(k), where s(1)=1, s(j)=22*s(j-1)+j.
• A014877 (program): Inverse of 868th cyclotomic polynomial.
• A014881 (program): a(1)=1, a(n) = 11*a(n-1)+n.
• A014882 (program): a(1) = 1, a(n) = 12*a(n-1) + n.
• A014896 (program): a(1) = 1, a(n) = 13*a(n-1) + n.
• A014897 (program): a(1)=1, a(n) = 14*a(n-1) + n.
• A014898 (program): a(1)=1, a(n) = 15*a(n-1) + n.
• A014899 (program): a(n) = (16^(n+1) - 15*n - 16)/225.
• A014900 (program): a(1)=1, a(n)=17*a(n-1)+n.
• A014901 (program): a(1)=1, a(n) = 18*a(n-1) + n.
• A014903 (program): a(1)=1, a(n) = 19*a(n-1) + n.
• A014904 (program): a(1)=1, a(n) = 20*a(n-1) + n.
• A014905 (program): a(1)=1, a(n) = 21*a(n-1) + n.
• A014907 (program): a(1)=1, a(n) = 22*a(n-1) + n.
• A014909 (program): a(1)=1, a(n) = 23*a(n-1) + n.
• A014913 (program): a(1)=1, a(n) = 24*a(n-1) + n.
• A014914 (program): a(1)=1, a(n) = 25*a(n-1) + n.
• A014915 (program): a(1)=1, a(n) = n*3^(n-1) + a(n-1).
• A014916 (program): a(1)=1, a(n) = n*4^(n-1) + a(n-1).
• A014917 (program): a(1)=1, a(n) = n*5^(n-1) + a(n-1).
• A014918 (program): a(1)=1, a(n) = n*6^(n-1) + a(n-1).
• A014920 (program): a(1)=1, a(n) = n*7^(n-1) + a(n-1).
• A014921 (program): a(1)=1, a(n) = n*8^(n-1) + a(n-1).
• A014923 (program): a(1) = 1, a(n) = n*9^(n-1) + a(n-1).
• A014925 (program): Number of zeros in numbers 1 to 111…1 (n+1 digits).
• A014926 (program): a(1)=1, a(n) = n*11^(n-1) + a(n-1).
• A014927 (program): a(1)=1, a(n) = n*12^(n-1) + a(n-1).
• A014928 (program): a(1)=1, a(n)=n*13^(n-1)+a(n-1).
• A014929 (program): a(1)=1, a(n) = n*14^(n-1) + a(n-1).
• A014930 (program): a(1)=1, a(n) = n*15^(n-1) + a(n-1).
• A014931 (program): a(1)=1, a(n) = n*16^(n-1) + a(n-1).
• A014934 (program): a(1)=1, a(n)=n*17^(n-1)+a(n-1).
• A014935 (program): a(1)=1, a(n) = n*18^(n-1) + a(n-1).
• A014936 (program): a(1)=1, a(n) = n*19^(n-1) + a(n-1).
• A014937 (program): a(1)=1, a(n)=n*20^(n-1)+a(n-1).
• A014938 (program): a(1)=1, a(n) = n*21^(n-1) + a(n-1).
• A014940 (program): a(1)=1, a(n)=n*22^(n-1)+a(n-1).
• A014941 (program): a(1)=1, a(n) = n*23^(n-1) + a(n-1).
• A014942 (program): ( 1+24^n*(23*n-1) ) / 529.
• A014943 (program): a(1)=1, a(n)=n*25^(n-1)+a(n-1).
• A014961 (program): Inverse of 952nd cyclotomic polynomial.
• A014963 (program): Exponential of Mangoldt function M(n): a(n) = 1 unless n is a prime or prime power when a(n) = that prime.
• A014964 (program): a(n) = lcm(n, 2^(n-1)).
• A014965 (program): a(n) = lcm(n, Fibonacci(n)).
• A014968 (program): Expansion of (1/theta_4 - 1)/2.
• A014969 (program): Expansion of (theta_3(q) / theta_4(q))^2 in powers of q.
• A014972 (program): Expansion of (theta_3(q) / theta_4(q) )^4 in powers of q; also of 1 / (1 - lambda(z)).
• A014973 (program): a(n) = n / gcd(n, (n-1)!).
• A014977 (program): Expansion of Molien series for automorphism group (2.Weyl(E6)) of E6 lattice.
• A014979 (program): Numbers that are both triangular and pentagonal.
• A014980 (program): a(n+1) = floor(a(n)/2) * ceiling(a(n)/2), a(0) = 5.
• A014981 (program): a(n) = c(prime(n))/prime(n), where c = Perrin sequence A001608 (starting 0,2,3,…) and prime(n) is the n-th prime.
• A014983 (program): a(n) = (1 - (-3)^n)/4.
• A014985 (program): a(n) = (1 - (-4)^n)/5.
• A014986 (program): a(n) = (1 - (-5)^n)/6.
• A014987 (program): a(n) = (1 - (-6)^n)/7.
• A014989 (program): a(n) = (1 - (-7)^n)/8.
• A014990 (program): a(n) = (1 - (-8)^n)/9.
• A014991 (program): a(n) = (1 - (-9)^n)/10.
• A014992 (program): a(n) = (1 - (-10)^n)/11.
• A014993 (program): a(n) = (1 - (-11)^n)/12.
• A014994 (program): a(n) = (1 - (-12)^n)/13.
• A015000 (program): q-integers for q=-13.
• A015001 (program): q-factorial numbers for q=3.
• A015002 (program): q-factorial numbers for q=4.
• A015003 (program): Inverse of 994th cyclotomic polynomial.
• A015004 (program): q-factorial numbers for q=5.
• A015005 (program): q-factorial numbers for q=6.
• A015006 (program): q-factorial numbers for q=7.
• A015007 (program): q-factorial numbers for q=8.
• A015008 (program): q-factorial numbers for q=9.
• A015009 (program): q-factorial numbers for q=10.
• A015011 (program): q-factorial numbers for q=11.
• A015013 (program): q-factorial numbers for q=-2.
• A015015 (program): q-factorial numbers for q=-3.
• A015017 (program): q-factorial numbers for q=-4.
• A015018 (program): q-factorial numbers for q=-5.
• A015019 (program): q-factorial numbers for q=-6.
• A015020 (program): q-factorial numbers for q=-7.
• A015022 (program): q-factorial numbers for q=-8.
• A015023 (program): q-factorial numbers for q=-9.
• A015025 (program): q-factorial numbers for q=-10.
• A015026 (program): q-factorial numbers for q=-11.
• A015027 (program): q-factorial numbers for q=-12.
• A015030 (program): q-Catalan numbers (binomial version) for q=2.
• A015045 (program): Inverse of 1036th cyclotomic polynomial.
• A015049 (program): Let m = A013929(n); then a(n) = smallest k such that m divides k^2.
• A015050 (program): Let m = A013929(n); then a(n) = smallest k such that m divides k^3.
• A015051 (program): Let m = A013929(n); then a(n) = smallest k such that m divides k^4.
• A015052 (program): a(n) is the smallest positive integer m such that m^5 is divisible by n.
• A015053 (program): Smallest positive integer for which n divides a(n)^6.
• A015073 (program): Inverse of 1064th cyclotomic polynomial.
• A015120 (program): Inverse of 1111th cyclotomic polynomial.
• A015128 (program): Number of overpartitions of n: an overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each integer may be overlined.
• A015142 (program): Inverse of 1133rd cyclotomic polynomial.
• A015152 (program): Sum of (Gaussian) q-binomial coefficients for q=-2.
• A015154 (program): Sum of (Gaussian) q-binomial coefficients for q=-3.
• A015155 (program): Sum of (Gaussian) q-binomial coefficients for q=-4.
• A015157 (program): Inverse of 1148th cyclotomic polynomial.
• A015167 (program): Sum of (Gaussian) q-binomial coefficients for q=-5.
• A015169 (program): Sum of (Gaussian) q-binomial coefficients for q=-6.
• A015170 (program): Sum of (Gaussian) q-binomial coefficients for q=-7.
• A015172 (program): Sum of (Gaussian) q-binomial coefficients for q=-8.
• A015173 (program): Sum of (Gaussian) q-binomial coefficients for q=-9.
• A015174 (program): Sum of (Gaussian) q-binomial coefficients for q=-10.
• A015176 (program): Sum of (Gaussian) q-binomial coefficients for q=-11.
• A015177 (program): Sum of (Gaussian) q-binomial coefficients for q=-12.
• A015178 (program): Sum of (Gaussian) q-binomial coefficients for q=-13.
• A015180 (program): Sum of (Gaussian) q-binomial coefficients for q=-14.
• A015181 (program): Sum of (Gaussian) q-binomial coefficients for q=-15.
• A015183 (program): Sum of (Gaussian) q-binomial coefficients for q=-16.
• A015184 (program): Sum of (Gaussian) q-binomial coefficients for q=-17.
• A015185 (program): Sum of (Gaussian) q-binomial coefficients for q=-18.
• A015186 (program): Inverse of 1177th cyclotomic polynomial.
• A015188 (program): Sum of (Gaussian) q-binomial coefficients for q=-19.
• A015189 (program): Sum of (Gaussian) q-binomial coefficients for q=-20.
• A015190 (program): Sum of (Gaussian) q-binomial coefficients for q=-21.
• A015191 (program): Sum of (Gaussian) q-binomial coefficients for q=-22.
• A015192 (program): Sum of (Gaussian) q-binomial coefficients for q=-23.
• A015193 (program): Sum of (Gaussian) q-binomial coefficients for q=-24.
• A015195 (program): Sum of Gaussian binomial coefficients for q=9.
• A015196 (program): Sum of Gaussian binomial coefficients for q=10.
• A015197 (program): Sum of Gaussian binomial coefficients for q=11.
• A015200 (program): Sum of Gaussian binomial coefficients for q=12.
• A015201 (program): Sum of Gaussian binomial coefficients for q=13.
• A015202 (program): Sum of Gaussian binomial coefficients for q=14.
• A015203 (program): Sum of Gaussian binomial coefficients for q=15.
• A015204 (program): Sum of Gaussian binomial coefficients for q=16.
• A015207 (program): Sum of Gaussian binomial coefficients for q=17.
• A015208 (program): Inverse of 1199th cyclotomic polynomial.
• A015209 (program): Sum of Gaussian binomial coefficients for q=18.
• A015210 (program): Sum of Gaussian binomial coefficients for q=19.
• A015211 (program): Sum of Gaussian binomial coefficients for q=20.
• A015212 (program): Sum of Gaussian binomial coefficients for q=21.
• A015213 (program): Inverse of 1204th cyclotomic polynomial.
• A015214 (program): Sum of Gaussian binomial coefficients for q=22.
• A015215 (program): Sum of Gaussian binomial coefficients for q=23.
• A015217 (program): Sum of Gaussian binomial coefficients for q=24.
• A015219 (program): Odd tetrahedral numbers: a(n) = (4*n+1)*(4*n+2)*(4*n+3)/6.
• A015220 (program): Even tetrahedral numbers.
• A015221 (program): Odd square pyramidal numbers.
• A015222 (program): Even square pyramidal numbers.
• A015223 (program): Odd pentagonal pyramidal numbers.
• A015224 (program): Even pentagonal pyramidal numbers.
• A015225 (program): Odd hexagonal pyramidal numbers.
• A015226 (program): Even hexagonal pyramidal numbers.
• A015234 (program): a(n) = (17 - 2*n)*n^2.
• A015237 (program): a(n) = (2*n - 1)*n^2.
• A015238 (program): a(n) = (2*n - 3)n^2.
• A015240 (program): a(n) = (2*n - 5)n^2.
• A015241 (program): Inverse of 1232nd cyclotomic polynomial.
• A015242 (program): a(n) = (2*n - 7)*n^2.
• A015243 (program): a(n) = (2*n - 9)*n^2.
• A015245 (program): a(n) = (2*n - 11)*n^2.
• A015246 (program): a(n) = (2*n - 13)*n^2.
• A015247 (program): a(n) = (2*n - 15)*n^2.
• A015249 (program): Gaussian binomial coefficient [ n,2 ] for q = -2.
• A015251 (program): Gaussian binomial coefficient [ n,2 ] for q = -3.
• A015252 (program): Inverse of 1243rd cyclotomic polynomial.
• A015253 (program): Gaussian binomial coefficient [ n,2 ] for q = -4.
• A015255 (program): Gaussian binomial coefficient [ n,2 ] for q = -5.
• A015257 (program): Gaussian binomial coefficient [ n,2 ] for q = -6.
• A015258 (program): Gaussian binomial coefficient [ n,2 ] for q = -7.
• A015259 (program): Gaussian binomial coefficient [ n,2 ] for q = -8.
• A015260 (program): Gaussian binomial coefficient [ n,2 ] for q = -9.
• A015261 (program): Gaussian binomial coefficient [ n,2 ] for q = -10.
• A015262 (program): Gaussian binomial coefficient [ n,2 ] for q = -11.
• A015264 (program): Gaussian binomial coefficient [ n,2 ] for q = -12.
• A015265 (program): Gaussian binomial coefficient [ n,2 ] for q = -13.
• A015266 (program): Gaussian binomial coefficient [ n,3 ] for q = -2.
• A015268 (program): Gaussian binomial coefficient [ n,3 ] for q = -3.
• A015271 (program): Gaussian binomial coefficient [ n,3 ] for q = -4.
• A015272 (program): Gaussian binomial coefficient [ n,3 ] for q = -5.
• A015273 (program): Gaussian binomial coefficient [ n,3 ] for q=-6.
• A015275 (program): Gaussian binomial coefficient [ n,3 ] for q = -7.
• A015276 (program): Gaussian binomial coefficient [ n,3 ] for q = -8.
• A015277 (program): Gaussian binomial coefficient [ n,3 ] for q = -9.
• A015278 (program): Gaussian binomial coefficient [ n,3 ] for q = -10.
• A015279 (program): Gaussian binomial coefficient [ n,3 ] for q = -11.
• A015281 (program): Gaussian binomial coefficient [ n,3 ] for q = -12.
• A015286 (program): Gaussian binomial coefficient [ n,3 ] for q = -13.
• A015287 (program): Gaussian binomial coefficient [ n,4 ] for q = -2.
• A015288 (program): Gaussian binomial coefficient [ n,4 ] for q = -3.
• A015289 (program): Gaussian binomial coefficient [ n,4 ] for q = -4.
• A015291 (program): Gaussian binomial coefficient [ n,4 ] for q = -5.
• A015292 (program): Gaussian binomial coefficient [ n,4 ] for q = -6.
• A015293 (program): Gaussian binomial coefficient [ n,4 ] for q = -7.
• A015294 (program): Gaussian binomial coefficient [ n,4 ] for q = -8.
• A015295 (program): Gaussian binomial coefficient [ n,4 ] for q = -9.
• A015297 (program): Inverse of 1288th cyclotomic polynomial.
• A015305 (program): Gaussian binomial coefficient [ n,5 ] for q = -2.
• A015306 (program): Gaussian binomial coefficient [ n,5 ] for q = -3.
• A015308 (program): Gaussian binomial coefficient [ n,5 ] for q = -4.
• A015309 (program): Gaussian binomial coefficient [ n,5 ] for q = -5.
• A015310 (program): Gaussian binomial coefficient [ n,5 ] for q = -6.
• A015322 (program): Inverse of 1313th cyclotomic polynomial.
• A015323 (program): Gaussian binomial coefficient [ n,6 ] for q = -2.
• A015324 (program): Gaussian binomial coefficient [ n,6 ] for q = -3.
• A015325 (program): Inverse of 1316th cyclotomic polynomial.
• A015326 (program): Gaussian binomial coefficient [ n,6 ] for q = -4.
• A015338 (program): Gaussian binomial coefficient [ n,7 ] for q = -2.
• A015340 (program): Gaussian binomial coefficient [ n,7 ] for q = -3.
• A015348 (program): Inverse of 1339th cyclotomic polynomial.
• A015356 (program): Gaussian binomial coefficient [ n,8 ] for q=-2.
• A015357 (program): Gaussian binomial coefficient [ n,8 ] for q=-3.
• A015371 (program): Gaussian binomial coefficient [ n,9 ] for q=-2.
• A015375 (program): Gaussian binomial coefficient [ n,9 ] for q=-3.
• A015400 (program): Inverse of 1391st cyclotomic polynomial.
• A015406 (program): Inverse of 1397th cyclotomic polynomial.
• A015426 (program): Inverse of 1417th cyclotomic polynomial.
• A015440 (program): Generalized Fibonacci numbers.
• A015441 (program): Generalized Fibonacci numbers.
• A015442 (program): Generalized Fibonacci numbers: a(n) = a(n-1) + 7*a(n-2), a(0)=0, a(1)=1.
• A015443 (program): Generalized Fibonacci numbers: a(n) = a(n-1) + 8*a(n-2).
• A015445 (program): Generalized Fibonacci numbers: a(n) = a(n-1) + 9*a(n-2).
• A015446 (program): Generalized Fibonacci numbers: a(n) = a(n-1) + 10*a(n-2).
• A015447 (program): Generalized Fibonacci numbers: a(n) = a(n-1) + 11*a(n-2).
• A015448 (program): a(0) = 1, a(1) = 1, and a(n) = 4*a(n-1) + a(n-2) for n >= 2.
• A015449 (program): Expansion of (1-4*x)/(1-5*x-x^2).
• A015450 (program): Inverse of 1441st cyclotomic polynomial.
• A015451 (program): a(n) = 6*a(n-1) + a(n-2) for n > 1, with a(0) = a(1) = 1.
• A015453 (program): Generalized Fibonacci numbers.
• A015454 (program): Generalized Fibonacci numbers.
• A015455 (program): a(n) = 9*a(n-1) + a(n-2) for n>1; a(0) = a(1) = 1.
• A015456 (program): Generalized Fibonacci numbers.
• A015457 (program): Generalized Fibonacci numbers.
• A015459 (program): q-Fibonacci numbers for q=2.
• A015460 (program): q-Fibonacci numbers for q=3.
• A015461 (program): q-Fibonacci numbers for q=4.
• A015462 (program): q-Fibonacci numbers for q=5.
• A015463 (program): q-Fibonacci numbers for q=6.
• A015464 (program): q-Fibonacci numbers for q=7.
• A015465 (program): q-Fibonacci numbers for q=8.
• A015467 (program): q-Fibonacci numbers for q=9.
• A015468 (program): q-Fibonacci numbers for q=10.
• A015469 (program): q-Fibonacci numbers for q=11.
• A015470 (program): q-Fibonacci numbers for q=12.
• A015473 (program): q-Fibonacci numbers for q=2.
• A015474 (program): q-Fibonacci numbers for q=3.
• A015475 (program): q-Fibonacci numbers for q=4.
• A015476 (program): q-Fibonacci numbers for q=5.
• A015477 (program): q-Fibonacci numbers for q=6.
• A015478 (program): Inverse of 1469th cyclotomic polynomial.
• A015479 (program): q-Fibonacci numbers for q=7.
• A015480 (program): q-Fibonacci numbers for q=8.
• A015481 (program): q-Fibonacci numbers for q=9.
• A015482 (program): q-Fibonacci numbers for q=10.
• A015484 (program): q-Fibonacci numbers for q=11.
• A015485 (program): q-Fibonacci numbers for q=12.
• A015486 (program): a(0)=1, a(1)=2, a(n) = sum_{k=0}^{k=n-1} 2^k a(k).
• A015487 (program): a(0)=1, a(1)=3, a(n) = sum_{k=0}^{k=n-1} 3^k a(k).
• A015489 (program): a(0)=1, a(1)=4, a(n) = sum_{k=0}^{k=n-1} 4^k a(k).
• A015490 (program): a(0)=1, a(1)=5, a(n) = sum_{k=0}^{k=n-1} 5^k a(k).
• A015492 (program): a(0)=1, a(1)=6, a(n) = sum_{k=0}^{k=n-1} 6^k a(k).
• A015493 (program): Inverse of 1484th cyclotomic polynomial.
• A015495 (program): a(0)=1, a(1)=7, a(n) = sum_{k=0}^{k=n-1} 7^k a(k).
• A015496 (program): a(0)=1, a(1)=8, a(n) = sum_{k=0}^{k=n-1} 8^k a(k).
• A015497 (program): a(0)=1, a(1)=9, a(n) = sum_{k=0}^{k=n-1} 9^k a(k).
• A015498 (program): a(0)=1, a(1)=10, a(n) = sum_{k=0}^{k=n-1} 10^k a(k).
• A015499 (program): a(0)=1, a(1)=11, a(n) = sum_{k=0}^{k=n-1} 11^k a(k).
• A015501 (program): a(0)=1, a(1)=12, a(n) = sum_{k=0}^{k=n-1} 12^k a(k).
• A015502 (program): a(1)=1, a(n) = Sum_{k=1..n-1} (3^k-1)/2 * a(k).
• A015503 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (4^k-1)/3 a(k).
• A015506 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (5^k-1)/4 a(k).
• A015507 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (6^k-1)/5 a(k).
• A015508 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (7^k-1)/6 a(k).
• A015509 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (8^k-1)/7 a(k).
• A015511 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (9^k-1)/8 a(k).
• A015512 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (10^k-1)/9 a(k).
• A015513 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (11^k-1)/10 a(k).
• A015515 (program): a(1)=1, a(n) = sum_{k=1}^{k=n-1} (12^k-1)/11 a(k).
• A015516 (program): Inverse of 1507th cyclotomic polynomial.
• A015518 (program): a(n) = 2*a(n-1) + 3*a(n-2), with a(0)=0, a(1)=1.
• A015519 (program): a(n) = 2*a(n-1) + 7*a(n-2).
• A015520 (program): a(n) = 2*a(n-1) + 11*a(n-2), a(0) = 0, a(1) = 1.
• A015521 (program): a(n) = 3*a(n-1) + 4*a(n-2), a(0) = 0, a(1) = 1.
• A015523 (program): a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=0, a(1)=1.
• A015524 (program): a(n) = 3*a(n-1) + 7*a(n-2).
• A015525 (program): Expansion of x/(1-3*x-8*x^2).
• A015528 (program): a(n) = 3*a(n-1) + 10*a(n-2).
• A015529 (program): Expansion of x/(1 - 3*x - 11*x^2).
• A015530 (program): Expansion of x/(1 - 4*x - 3*x^2).
• A015531 (program): Linear 2nd order recurrence: a(n) = 4*a(n-1) + 5*a(n-2).
• A015532 (program): a(n) = 4*a(n-1) + 7*a(n-2).
• A015533 (program): a(n) = 4*a(n-1) + 9*a(n-2).
• A015534 (program): Expansion of x/(1 - 4*x - 11*x^2).
• A015535 (program): Expansion of x/(1 - 5*x - 2*x^2).
• A015536 (program): Expansion of x/(1-5*x-3*x^2).
• A015537 (program): Expansion of x/(1 - 5*x - 4*x^2).
• A015538 (program): Inverse of 1529th cyclotomic polynomial.
• A015540 (program): a(n) = 5*a(n-1) + 6*a(n-2), a(0) = 0, a(1) = 1.
• A015541 (program): Expansion of x/(1 - 5*x - 7*x^2).
• A015544 (program): Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1.
• A015545 (program): Expansion of x/(1 - 5*x - 9*x^2).
• A015547 (program): Expansion of x/(1 - 5*x - 11*x^2).
• A015548 (program): Expansion of x/(1 - 5*x - 12*x^2).
• A015551 (program): Expansion of x/(1 - 6*x - 5*x^2).
• A015552 (program): a(n) = 6*a(n-1) + 7*a(n-2), a(0) = 0, a(1) = 1.
• A015553 (program): Expansion of x/(1 - 6*x - 11*x^2).
• A015554 (program): a(n) = floor( (n/e)^n ).
• A015555 (program): Expansion of x/(1 - 7*x - 2*x^2).
• A015557 (program): a(n) = ceiling((n/e)^n).
• A015559 (program): Expansion of x/(1 - 7*x - 3*x^2).
• A015561 (program): Expansion of x/(1 - 7*x - 4*x^2).
• A015562 (program): Expansion of x/(1 - 7*x - 5*x^2).
• A015564 (program): Expansion of x/(1 - 7*x - 6*x^2).
• A015565 (program): a(n) = 7*a(n-1) + 8*a(n-2), a(0) = 0, a(1) = 1.
• A015566 (program): Expansion of x/(1 - 7*x - 9*x^2).
• A015568 (program): Expansion of x/(1 - 7*x - 10*x^2).
• A015570 (program): Expansion of x/(1 - 7*x - 11*x^2).
• A015572 (program): Expansion of x/(1 - 7*x - 12*x^2).
• A015574 (program): Expansion of x/(1 - 8*x - 3*x^2).
• A015575 (program): Expansion of x/(1 - 8*x - 5*x^2).
• A015576 (program): Expansion of x/(1 - 8*x - 7*x^2).
• A015577 (program): a(n+1) = 8*a(n) + 9*a(n-1), a(0) = 0, a(1) = 1.
• A015578 (program): Expansion of x/(1 - 8*x - 11*x^2).
• A015579 (program): Expansion of x/(1-9*x-2*x^2).
• A015580 (program): Expansion of x/(1 - 9*x - 4*x^2).
• A015581 (program): a(n) = 9*a(n-1) + 5*a(n-2).
• A015582 (program): Inverse of 1573rd cyclotomic polynomial.
• A015583 (program): a(0) = 0, a(1) = 1; for n >= 2, a(n) = 9*a(n-1) + 7*a(n-2).
• A015584 (program): Expansion of x/(1 - 9*x - 8*x^2).
• A015585 (program): a(n) = 9*a(n-1) + 10*a(n-2).
• A015587 (program): Expansion of x/(1 - 9*x - 11*x^2).
• A015588 (program): Expansion of x/(1 - 10*x - 3*x^2).
• A015589 (program): Expansion of x/(1 - 10*x - 7*x^2).
• A015591 (program): Expansion of x/(1 - 10*x - 9*x^2).
• A015592 (program): a(n) = 10*a(n-1) + 11*a(n-2).
• A015593 (program): a(n) = 11*a(n-1) + 2*a(n-2).
• A015594 (program): a(n) = 11*a(n-1) + 3*a(n-2).
• A015596 (program): a(n) = 11 a(n-1) + 4 a(n-2).
• A015597 (program): a(n) = 11 a(n-1) + 5 a(n-2).
• A015598 (program): a(n) = 11*a(n-1) + 6*a(n-2).
• A015601 (program): a(n) = 11*a(n-1) + 7*a(n-2).
• A015602 (program): a(n) = 11 a(n-1) + 8 a(n-2).
• A015603 (program): a(n) = 11*a(n-1) + 9*a(n-2).
• A015606 (program): a(n) = 11*a(n-1) + 10*a(n-2).
• A015609 (program): a(n) = 11*a(n-1) + 12*a(n-2).
• A015610 (program): a(n) = 12*a(n-1) + 5*a(n-2) for n >= 2, a(0) = 0, a(1) = 1.
• A015611 (program): a(n) = 12*a(n-1) + 7*a(n-2).
• A015612 (program): a(n) = 12*a(n-1) + 11*a(n-2).
• A015613 (program): a(n) = Sum_{i=1..n} phi(i) * (ceiling(n/i) - floor(n/i)).
• A015614 (program): a(n) = -1 + Sum_{i=1..n} phi(i).
• A015616 (program): Number of triples (i,j,k) with 1 <= i < j < k <= n and gcd(i,j,k) = 1.
• A015618 (program): Number of triples of different integers from [ 2,n ] with no global factor.
• A015631 (program): Number of ordered triples of integers from [ 1..n ] with no global factor.
• A015633 (program): Number of ordered triples of integers from [ 2,n ] with no global factor.
• A015648 (program): Inverse of 1639th cyclotomic polynomial.
• A015660 (program): Inverse of 1651st cyclotomic polynomial.
• A015661 (program): Inverse of 1652nd cyclotomic polynomial.
• A015664 (program): Expansion of e.g.f. theta_3^(1/2).
• A015665 (program): Expansion of e.g.f. theta_3^(3/2).
• A015666 (program): Expansion of e.g.f. theta_3^(5/2).
• A015667 (program): Expansion of e.g.f. theta_3^(7/2).
• A015669 (program): Expansion of e.g.f. theta_3^(9/2).
• A015670 (program): Inverse of 1661st cyclotomic polynomial.
• A015671 (program): Expansion of e.g.f. theta_3^(11/2).
• A015672 (program): Expansion of e.g.f. theta_3^(13/2).
• A015673 (program): Expansion of e.g.f. theta_3^(15/2).
• A015675 (program): Expansion of e.g.f. theta_3^(17/2).
• A015676 (program): Expansion of e.g.f. theta_3^(19/2).
• A015677 (program): Expansion of e.g.f. theta_3^(21/2).
• A015678 (program): Expansion of e.g.f. theta_3^(23/2).
• A015679 (program): Expansion of e.g.f. theta_3^(25/2).
• A015680 (program): Expansion of e.g.f. theta_3^(-1/2).
• A015682 (program): Expansion of e.g.f. theta_3^(-3/2).
• A015683 (program): Expansion of e.g.f. theta_3^(-5/2).
• A015684 (program): Expansion of e.g.f. theta_3^(-7/2).
• A015685 (program): Expansion of e.g.f. theta_3^(-9/2).
• A015687 (program): Expansion of e.g.f. theta_3^(-11/2).
• A015690 (program): Expansion of e.g.f. theta_3^(-13/2).
• A015691 (program): Expansion of e.g.f. theta_3^(-15/2).
• A015693 (program): Expansion of e.g.f. theta_3^(-17/2).
• A015694 (program): Expansion of e.g.f. theta_3^(-19/2).
• A015695 (program): Expansion of e.g.f. theta_3^(-21/2).
• A015696 (program): Expansion of e.g.f. theta_3^(-23/2).
• A015697 (program): Expansion of e.g.f. theta_3^(-25/2).
• A015712 (program): Inverse of 1703rd cyclotomic polynomial.
• A015717 (program): Inverse of 1708th cyclotomic polynomial.
• A015726 (program): Inverse of 1717th cyclotomic polynomial.
• A015732 (program): Even numbers k such that d(k) | phi(k).
• A015733 (program): d(n) does not divide phi(n).
• A015734 (program): Odd n such that d(n) does not divide phi(n).
• A015736 (program): Inverse of 1727th cyclotomic polynomial.
• A015760 (program): Inverse of 1751st cyclotomic polynomial.
• A015777 (program): Inverse of 1768th cyclotomic polynomial.
• A015790 (program): Inverse of 1781st cyclotomic polynomial.
• A015802 (program): Inverse of 1793rd cyclotomic polynomial.
• A015816 (program): Inverse of 1807th cyclotomic polynomial.
• A015828 (program): Inverse of 1819th cyclotomic polynomial.
• A015846 (program): Inverse of 1837th cyclotomic polynomial.
• A015862 (program): Inverse of 1853rd cyclotomic polynomial.
• A015868 (program): Inverse of 1859th cyclotomic polynomial.
• A015885 (program): Inverse of 1876th cyclotomic polynomial.
• A015910 (program): a(n) = 2^n mod n.
• A015911 (program): Numbers k such that 2^k mod k is odd.
• A015912 (program): Inverse of 1903rd cyclotomic polynomial.
• A015913 (program): Numbers k such that sigma(k) + 4 = sigma(k+4).
• A015916 (program): Numbers k such that sigma(k) + 10 = sigma(k+10).
• A015919 (program): Positive integers k such that 2^k == 2 (mod k).
• A015921 (program): Positive integers n such that 2^n == 4 (mod n).
• A015928 (program): Inverse of 1919th cyclotomic polynomial.
• A015930 (program): Inverse of 1921st cyclotomic polynomial.
• A015943 (program): (2^(2n)+n) mod (2n).
• A015946 (program): Inverse of 1937th cyclotomic polynomial.
• A015966 (program): Inverse of 1957th cyclotomic polynomial.
• A015972 (program): Inverse of 1963rd cyclotomic polynomial.
• A015978 (program): Inverse of 1969th cyclotomic polynomial.
• A015993 (program): Twelve iterations of Reverse and Add are needed to reach a palindrome.
• A015995 (program): a(n) = (tau(n^3)+2)/3.
• A015996 (program): (tau(n^4) + 3)/4, where tau = A000005.
• A015997 (program): Inverse of 1988th cyclotomic polynomial.
• A015999 (program): a(n) = (tau(n^5) + 4)/5.
• A016000 (program): Inverse of 1991st cyclotomic polynomial.
• A016001 (program): a(n) = (tau(n^6)+5)/6.
• A016002 (program): a(n) = (tau(n^7)+6)/7.
• A016003 (program): a(n) = (tau(n^8)+7)/8.
• A016005 (program): a(n) = (tau(n^9)+8)/9.
• A016006 (program): a(n) = (tau(n^10)+9)/10.
• A016007 (program): a(n) = (tau(n^11)+10)/11.
• A016008 (program): a(n) = (tau(n^12)+11)/12.
• A016009 (program): a(n) = (tau(n^13)+12)/13.
• A016012 (program): a(n) = (tau(n^n)+n-1)/n.
• A016014 (program): Least k such that 2*n*k + 1 is a prime.
• A016017 (program): Smallest k such that 1/k can be written as a sum of exactly 2 unit fractions in n ways.
• A016028 (program): Expansion of (1 - x + x^4) / (1 - x)^3.
• A016029 (program): a(1) = a(2) = 1, a(2n + 1) = 2*a(2n) and a(2n) = 2*a(2n - 1) + (-1)^n.
• A016035 (program): a(n) = Sum_{j|n, 1 < j < n} phi(j). Also a(n) = n - phi(n) - 1 for n > 1.
• A016042 (program): Inverse of 2033rd cyclotomic polynomial.
• A016043 (program): 2^(2^n) +- 1 without repeats.
• A016050 (program): Inverse of 2041st cyclotomic polynomial.
• A016051 (program): Numbers of the form 9*k+3 or 9*k+6.
• A016052 (program): a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits.
• A016053 (program): Inverse of 2044th cyclotomic polynomial.
• A016061 (program): a(n) = n*(n+1)*(4*n+5)/6.
• A016064 (program): Smallest side lengths of almost-equilateral Heronian triangles (sides are consecutive positive integers, area is a nonnegative integer).
• A016065 (program): a(n) = Sum_{k=0..n} k!*(k+1)!.
• A016071 (program): Description to be supplied!.
• A016075 (program): Expansion of 1/((1-8*x)*(1-9*x)*(1-10*x)*(1-11*x)).
• A016080 (program): Inverse of 2071st cyclotomic polynomial.
• A016081 (program): Add 4, then reverse digits; start with 3.
• A016082 (program): Add 4, then reverse the decimal digits; start with 10.
• A016084 (program): a(n+1) = a(n) + its digital root.
• A016090 (program): a(n) = 16^(5^n) mod 10^n: Automorphic numbers ending in digit 6, with repetitions.
• A016091 (program): Expansion of 1/((1-8x)(1-9x)(1-10x)(1-12x)).
• A016092 (program): Expansion of 1/((1-8x)(1-9x)(1-11x)(1-12x)).
• A016093 (program): Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).
• A016094 (program): Expansion of 1/((1-9x)(1-10x)(1-11x)(1-12x)).
• A016095 (program): Triangular array T(n,k) read by rows, where T(n,k) = coefficient of x^n*y^k in 1/(1-x-y-(x+y)^2).
• A016096 (program): a(n+1) = a(n) + sum of its digits, with a(1) = 9.
• A016098 (program): Number of crossing set partitions of {1,2,…,n}.
• A016101 (program): (n! - n)/2 for even n.
• A016103 (program): Expansion of 1/((1-4x)(1-5x)(1-6x)).
• A016105 (program): Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4).
• A016109 (program): Expansion of 1/((1-7x)(1-8x)(1-9x)(1-10x)).
• A016110 (program): Inverse of 2101st cyclotomic polynomial.
• A016111 (program): Expansion of 1/((1-11x)(1-12x)(1-13x)(1-14x)(1-15x)).
• A016116 (program): a(n) = 2^floor(n/2).
• A016123 (program): a(n) = (11^(n+1) - 1)/10.
• A016125 (program): Expansion of 1/((1-x)*(1-12*x)).
• A016127 (program): Expansion of 1/((1-2*x)*(1-5*x)).
• A016128 (program): Inverse of 2119th cyclotomic polynomial.
• A016129 (program): Expansion of 1/((1-2x)(1-6x)).
• A016130 (program): Expansion of 1/((1-2x)(1-7x)).
• A016131 (program): Expansion of 1/((1-2x)(1-8x)).
• A016132 (program): Inverse of 2123rd cyclotomic polynomial.
• A016133 (program): Expansion of 1/((1-2*x)*(1-9*x)).
• A016134 (program): Expansion of 1/((1-2x)(1-10x)).
• A016135 (program): Expansion of 1/((1-2*x)*(1-11*x)).
• A016136 (program): Expansion of 1/((1-2*x)*(1-12*x)).
• A016137 (program): Expansion of 1/((1-3x)(1-6x)).
• A016138 (program): Expansion of 1/((1-3x)(1-7x)).
• A016140 (program): Expansion of 1/((1-3x)(1-8x)).
• A016142 (program): Expansion of 1/((1-3x)(1-9x)).
• A016145 (program): Expansion of 1/((1-3x)(1-10x)).
• A016146 (program): Expansion of 1/((1-3x)(1-11x)).
• A016147 (program): Expansion of 1/((1-3x)(1-12x)).
• A016149 (program): Expansion of 1/((1-4*x)*(1-6*x)).
• A016150 (program): Expansion of 1/((1-4x)(1-7x)).
• A016152 (program): a(n) = 4^(n-1)*(2^n-1).
• A016153 (program): a(n) = (9^n-4^n)/5.
• A016156 (program): Inverse of 2147th cyclotomic polynomial.
• A016157 (program): Expansion of 1/((1-4x)(1-10x)).
• A016158 (program): Expansion of 1/((1-4*x)(1-11*x)).
• A016159 (program): Expansion of 1/((1-4x)(1-12x)).
• A016161 (program): Expansion of 1/((1-5x)(1-7x)).
• A016162 (program): Expansion of 1/((1-5x)(1-8x)).
• A016163 (program): Expansion of 1/((1-5x)(1-9x)).
• A016164 (program): Expansion of 1/((1-5x)(1-10x)).
• A016165 (program): Expansion of 1/((1-5x)(1-11x)).
• A016166 (program): Expansion of 1/((1-5x)(1-12x)).
• A016168 (program): Inverse of 2159th cyclotomic polynomial.
• A016169 (program): a(n) = 7^n - 6^n.
• A016170 (program): Expansion of 1/((1-6x)(1-8x)).
• A016172 (program): Expansion of 1/((1-6x)(1-9x)).
• A016173 (program): Expansion of 1/((1-6x)(1-10x)).
• A016174 (program): Expansion of 1/((1-6x)(1-11x)).
• A016175 (program): Expansion of 1/((1-6x)(1-12x)).
• A016176 (program): Inverse of 2167th cyclotomic polynomial.
• A016177 (program): a(n) = 8^n - 7^n.
• A016178 (program): Expansion of 1/((1-7x)(1-9x)).
• A016180 (program): Inverse of 2171st cyclotomic polynomial.
• A016181 (program): Expansion of 1/((1-7x)(1-10x)).
• A016183 (program): Expansion of 1/((1-7x)(1-11x)).
• A016184 (program): Expansion of 1/((1-7x)(1-12x)).
• A016185 (program): a(n) = 9^n - 8^n.
• A016186 (program): Expansion of 1/((1-8x)(1-10x)).
• A016187 (program): Expansion of 1/((1-8x)(1-11x)).
• A016188 (program): Expansion of 1/((1-8x)*(1-12x)).
• A016189 (program): a(n) = 10^n - 9^n.
• A016190 (program): Expansion of 1/((1-9x)(1-11x)).
• A016191 (program): Expansion of 1/((1-9x)*(1-12x)).
• A016195 (program): a(n) = 11^n - 10^n.
• A016196 (program): Expansion of 1/((1-10x)*(1-12x)).
• A016197 (program): a(n) = 12^n - 11^n.
• A016198 (program): Expansion of 1/((1-x)(1-2x)(1-5x)).
• A016200 (program): Expansion of 1/((1-x)(1-2x)(1-6x)).
• A016201 (program): Expansion of 1/((1-x)(1-2x)(1-7x)).
• A016203 (program): Expansion of 1/((1-x)(1-2x)(1-8x)).
• A016204 (program): Expansion of 1/((1-x)(1-2x)(1-9x)).
• A016205 (program): Expansion of 1/((1-x)(1-2x)(1-10x)).
• A016206 (program): Expansion of 1/((1-x)*(1-2x)*(1-11x)).
• A016207 (program): Expansion of 1/((1-x)(1-2x)(1-12x)).
• A016208 (program): Expansion of 1/((1-x)*(1-3*x)*(1-4*x)).
• A016209 (program): Expansion of 1/((1-x)(1-3x)(1-5x)).
• A016211 (program): Expansion of 1/((1-x)(1-3x)(1-6x)).
• A016212 (program): Expansion of 1/((1-x)*(1-3*x)*(1-7*x)).
• A016214 (program): Expansion of 1/((1-x)(1-3x)(1-8x)).
• A016215 (program): Expansion of 1/((1-x)(1-3x)(1-10x)).
• A016216 (program): Expansion of 1/((1-x)(1-3x)(1-11x)).
• A016217 (program): Expansion of 1/((1-x)(1-3x)(1-12x)).
• A016218 (program): Expansion of 1/((1-x)*(1-4*x)*(1-5*x)).
• A016221 (program): Inverse of 2212th cyclotomic polynomial.
• A016222 (program): Expansion of 1/((1-x)(1-4x)(1-6x)).
• A016223 (program): Expansion of 1/((1-x)(1-4x)(1-7x)).
• A016224 (program): Expansion of 1/((1-x)(1-4x)(1-8x)).
• A016225 (program): Expansion of 1/((1-x)(1-4x)(1-10x)).
• A016226 (program): Expansion of 1/((1-x)(1-4x)(1-11x)).
• A016227 (program): Expansion of 1/((1-x)(1-4x)(1-12x)).
• A016228 (program): Expansion of 1/((1-x)*(1-5*x)(1-6*x)).
• A016230 (program): Expansion of 1/((1-x)(1-5x)(1-7x)).
• A016231 (program): Inverse of 2222nd cyclotomic polynomial.
• A016233 (program): Expansion of 1/((1-x)(1-5x)(1-8x)).
• A016234 (program): Expansion of 1/((1-x)(1-5x)(1-9x)).
• A016236 (program): Inverse of 2227th cyclotomic polynomial.
• A016237 (program): Expansion of 1/((1-x)(1-5x)(1-10x)).
• A016238 (program): Expansion of 1/((1-x)*(1-5*x)*(1-11*x)).
• A016239 (program): Expansion of 1/((1-x)*(1-5*x)*(1-12*x)).
• A016241 (program): Expansion of 1/((1-x)*(1-6*x)*(1-7*x)).
• A016243 (program): Expansion of 1/((1-x)*(1-6*x)*(1-8*x)).
• A016244 (program): Expansion of 1/((1-x)*(1-6*x)*(1-9*x)).
• A016246 (program): Expansion of 1/((1-x)(1-6x)(1-10x)).
• A016247 (program): Expansion of 1/((1-x)(1-6x)(1-11x)).
• A016248 (program): Expansion of 1/((1-x)(1-6x)(1-12x)).
• A016249 (program): Expansion of 1/((1-x)*(1-7*x)*(1-8*x)).
• A016250 (program): Expansion of 1/((1-x)(1-7x)(1-9x)).
• A016252 (program): Expansion of 1/((1-x)*(1-7x)*(1-10x)).
• A016254 (program): Expansion of 1/((1-x)(1-7x)(1-11x)).
• A016255 (program): Expansion of 1/((1-x)(1-7x)(1-12x)).
• A016256 (program): Expansion of 1/((1-x)*(1-8*x)*(1-9*x)).
• A016257 (program): Expansion of 1/((1-x)(1-8x)(1-10x)).
• A016258 (program): Inverse of 2249th cyclotomic polynomial.
• A016259 (program): Expansion of 1/((1-x)(1-8x)(1-11x)).
• A016260 (program): Expansion of 1/((1-x)(1-8x)(1-12x)).
• A016261 (program): Expansion of 1/((1-x)*(1-9*x)*(1-10*x)).
• A016262 (program): Expansion of 1/((1-x)(1-9x)(1-11x)).
• A016263 (program): Expansion of 1/((1-x)(1-9x)(1-12x)).
• A016265 (program): Expansion of 1/((1-x)*(1-10x)*(1-11x)).
• A016267 (program): Expansion of 1/((1-x)(1-10x)(1-12x)).
• A016268 (program): Expansion of 1/((1-x)(1-11x)(1-12x)).
• A016269 (program): Number of monotone Boolean functions of n variables with 2 mincuts. Also number of Sperner systems with 2 blocks.
• A016273 (program): Expansion of 1/((1-2x)(1-3x)(1-5x)).
• A016275 (program): Inverse of 2266th cyclotomic polynomial.
• A016276 (program): Expansion of 1/((1-2x)(1-3x)(1-7x)).
• A016277 (program): Expansion of 1/((1-2x)(1-3x)(1-8x)).
• A016278 (program): Expansion of 1/((1-2x)(1-3x)(1-9x)).
• A016279 (program): Expansion of 1/((1-2x)(1-3x)(1-10x)).
• A016280 (program): Expansion of 1/((1-2x)(1-3x)(1-11x)).
• A016281 (program): Expansion of 1/((1-2x)(1-3x)(1-12x)).
• A016282 (program): Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)).
• A016283 (program): a(n) = 6^n/8 - 4^(n-1) + 2^(n-3).
• A016285 (program): Expansion of 1/((1-2x)(1-4x)(1-7x)).
• A016290 (program): Expansion of 1/((1-2x)(1-4x)(1-8x)).
• A016291 (program): Expansion of 1/((1-2x)*(1-4x)*(1-9x)).
• A016292 (program): Expansion of 1/((1-2x)*(1-4x)*(1-10x)).
• A016293 (program): Expansion of 1/((1-2x)(1-4x)(1-11x)).
• A016294 (program): Expansion of 1/((1-2x)(1-4x)(1-12x)).
• A016295 (program): Expansion of 1/((1-2x)(1-5x)(1-6x)).
• A016296 (program): Expansion of 1/((1-2x)(1-5x)(1-7x)).
• A016297 (program): Expansion of 1/((1-2x)(1-5x)(1-8x)).
• A016298 (program): Expansion of 1/((1-2x)(1-5x)(1-9x)).
• A016299 (program): Expansion of 1/((1-2*x)*(1-5*x)*(1-10*x)).
• A016301 (program): Expansion of 1/((1-2*x)*(1-5*x)*(1-11*x)).
• A016302 (program): Expansion of 1/((1-2*x)*(1-5*x)*(1-12*x)).
• A016304 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)).
• A016305 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)).
• A016306 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-9*x)).
• A016307 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-10*x)).
• A016308 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-11*x)).
• A016309 (program): Expansion of 1/((1-2*x)*(1-6*x)*(1-12*x)).
• A016311 (program): Expansion of 1/((1-2*x)*(1-7*x)*(1-8*x)).
• A016312 (program): Expansion of 1/((1-2x)*(1-7x)*(1-9x)).
• A016313 (program): Expansion of 1/((1-2x)(1-7x)(1-10x)).
• A016314 (program): Expansion of 1/((1-2x)*(1-7x)*(1-11x)).
• A016315 (program): Expansion of 1/((1-2x)*(1-7x)*(1-12x)).
• A016316 (program): Expansion of 1/((1-2x)*(1-8x)*(1-9x)).
• A016317 (program): Expansion of 1/((1-2x)(1-8x)(1-10x)).
• A016318 (program): Expansion of 1/((1-2x)(1-8x)(1-11x)).
• A016320 (program): Expansion of 1/((1-2x)(1-8x)(1-12x)).
• A016321 (program): Expansion of 1/((1-2x)(1-9x)(1-10x)).
• A016322 (program): Expansion of 1/((1-2x)(1-9x)(1-11x)).
• A016324 (program): Expansion of 1/((1-2x)(1-9x)(1-12x)).
• A016325 (program): Expansion of 1/((1-2x)(1-10x)(1-11x)).
• A016326 (program): Expansion of 1/((1-2x)(1-10x)(1-12x)).
• A016328 (program): 120th cyclotomic polynomial.
• A016329 (program): 126th cyclotomic polynomial.
• A016330 (program): 130th cyclotomic polynomial.
• A016331 (program): 132nd cyclotomic polynomial.
• A016332 (program): 133rd cyclotomic polynomial.
• A016333 (program): 138th cyclotomic polynomial.
• A016334 (program): 140th cyclotomic polynomial.
• A016335 (program): 143rd cyclotomic polynomial.
• A016336 (program): 145th cyclotomic polynomial.
• A016337 (program): 150th cyclotomic polynomial.
• A016338 (program): 154th cyclotomic polynomial.
• A016339 (program): 155th cyclotomic polynomial.
• A016340 (program): 156th cyclotomic polynomial.
• A016341 (program): 161st cyclotomic polynomial.
• A016343 (program): 168th cyclotomic polynomial.
• A016344 (program): 170th cyclotomic polynomial.
• A016345 (program): 174th cyclotomic polynomial.
• A016346 (program): 175th cyclotomic polynomial.
• A016347 (program): 180th cyclotomic polynomial.
• A016349 (program): 185th cyclotomic polynomial.
• A016350 (program): 186th cyclotomic polynomial.
• A016351 (program): 187th cyclotomic polynomial.
• A016352 (program): 190th cyclotomic polynomial.
• A016354 (program): 198th cyclotomic polynomial.
• A016355 (program): 203rd cyclotomic polynomial.
• A016356 (program): 209th cyclotomic polynomial.
• A016358 (program): 217th cyclotomic polynomial.
• A016360 (program): 221st cyclotomic polynomial.
• A016361 (program): 230th cyclotomic polynomial.
• A016363 (program): 238th cyclotomic polynomial.
• A016364 (program): 247th cyclotomic polynomial.
• A016365 (program): 253rd cyclotomic polynomial.
• A016367 (program): 259th cyclotomic polynomial.
• A016368 (program): 260th cyclotomic polynomial.
• A016369 (program): 266th cyclotomic polynomial.
• A016371 (program): 280th cyclotomic polynomial.
• A016373 (program): 286th cyclotomic polynomial.
• A016374 (program): 287th cyclotomic polynomial.
• A016375 (program): 290th cyclotomic polynomial.
• A016376 (program): 299th cyclotomic polynomial.
• A016377 (program): 301st cyclotomic polynomial.
• A016378 (program): 308th cyclotomic polynomial.
• A016379 (program): 310th cyclotomic polynomial.
• A016381 (program): 319th cyclotomic polynomial.
• A016382 (program): 322nd cyclotomic polynomial.
• A016383 (program): 323rd cyclotomic polynomial.
• A016384 (program): 329th cyclotomic polynomial.
• A016386 (program): 340th cyclotomic polynomial.
• A016387 (program): 341st cyclotomic polynomial.
• A016389 (program): 350th cyclotomic polynomial.
• A016392 (program): 370th cyclotomic polynomial.
• A016393 (program): 371st cyclotomic polynomial.
• A016394 (program): 374th cyclotomic polynomial.
• A016395 (program): 377th cyclotomic polynomial.
• A016396 (program): 380th cyclotomic polynomial.
• A016399 (program): 391st cyclotomic polynomial.
• A016401 (program): 403rd cyclotomic polynomial.
• A016402 (program): 406th cyclotomic polynomial.
• A016403 (program): 407th cyclotomic polynomial.
• A016404 (program): 413th cyclotomic polynomial.
• A016405 (program): 418th cyclotomic polynomial.
• A016407 (program): 427th cyclotomic polynomial.
• A016409 (program): 434th cyclotomic polynomial.
• A016411 (program): 437th cyclotomic polynomial.
• A016412 (program): 442nd cyclotomic polynomial.
• A016413 (program): 451st cyclotomic polynomial.
• A016418 (program): 473rd cyclotomic polynomial.
• A016419 (program): 476th cyclotomic polynomial.
• A016420 (program): 481st cyclotomic polynomial.
• A016422 (program): 493rd cyclotomic polynomial.
• A016423 (program): 494th cyclotomic polynomial.
• A016425 (program): 497th cyclotomic polynomial.
• A016426 (program): 506th cyclotomic polynomial.
• A016578 (program): Decimal expansion of log(3/2).
• A016580 (program): Decimal expansion of log(7/2).
• A016627 (program): Decimal expansion of log(4).
• A016628 (program): Decimal expansion of log(5).
• A016631 (program): Decimal expansion of log(8).
• A016632 (program): Decimal expansion of log(9).
• A016633 (program): Expansion of 1/((1-2x)(1-11x)(1-12x)).
• A016639 (program): Decimal expansion of log(16).
• A016648 (program): Decimal expansion of log(25).
• A016650 (program): Decimal expansion of log(27).
• A016655 (program): Decimal expansion of log(32) = 5*log(2).
• A016687 (program): Decimal expansion of log(64).
• A016704 (program): Decimal expansion of log(81).
• A016724 (program): Expansion of (2-2*x-x^2)/((1-2*x^2)*(1-x)^2).
• A016725 (program): Number of integer solutions to x^2+y^2+z^2 = n^2, allowing zeros and distinguishing signs and order.
• A016729 (program): Highest minimal Hamming distance of any Type 4^H+ Hermitian additive self-dual code over GF(4) of length n.
• A016742 (program): Even squares: a(n) = (2*n)^2.
• A016743 (program): Even cubes: a(n) = (2*n)^3.
• A016744 (program): a(n) = (2*n)^4.
• A016745 (program): a(n) = (2*n)^5.
• A016746 (program): a(n) = (2*n)^6.
• A016747 (program): a(n) = (2*n)^7.
• A016748 (program): a(n) = (2*n)^8.
• A016749 (program): a(n) = (2*n)^9.
• A016750 (program): a(n) = (2*n)^10.
• A016751 (program): a(n) = (2*n)^11.
• A016752 (program): a(n) = (2*n)^12.
• A016753 (program): Expansion of 1/((1-3*x)*(1-4*x)*(1-5*x)).
• A016754 (program): Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers.
• A016755 (program): Odd cubes: a(n) = (2*n + 1)^3.
• A016756 (program): a(n) = (2*n+1)^4.
• A016757 (program): a(n) = (2*n+1)^5.
• A016758 (program): a(n) = (2*n+1)^6.
• A016759 (program): a(n) = (2*n + 1)^7.
• A016760 (program): a(n) = (2*n+1)^8.
• A016761 (program): a(n) = (2*n+1)^9.
• A016762 (program): a(n) = (2*n + 1)^10.
• A016763 (program): a(n) = (2*n+1)^11.
• A016764 (program): a(n) = (2*n+1)^12.
• A016765 (program): Expansion of 1/((1-3*x)*(1-4*x)*(1-6*x)).
• A016766 (program): a(n) = (3*n)^2.
• A016767 (program): a(n) = (3*n)^3.
• A016768 (program): (3*n)^4.
• A016769 (program): a(n) = (3*n)^5.
• A016770 (program): a(n) = (3*n)^6.
• A016771 (program): a(n) = (3*n)^7.
• A016772 (program): a(n) = (3*n)^8.
• A016773 (program): a(n) = (3*n)^9.
• A016774 (program): a(n) = (3*n)^10.
• A016775 (program): (3*n)^11.
• A016776 (program): a(n) = (3*n)^12.
• A016777 (program): a(n) = 3*n + 1.
• A016778 (program): a(n) = (3*n+1)^2.
• A016779 (program): a(n) = (3*n + 1)^3.
• A016780 (program): a(n) = (3*n+1)^4.
• A016781 (program): a(n) = (3*n+1)^5.
• A016782 (program): a(n) = (3*n+1)^6.
• A016783 (program): a(n) = (3*n+1)^7.
• A016784 (program): a(n) = (3*n+1)^8.
• A016785 (program): a(n) = (3*n + 1)^9.
• A016786 (program): a(n) = (3*n+1)^10.
• A016787 (program): a(n) = (3*n + 1)^11.
• A016788 (program): a(n) = (3*n+1)^12.
• A016789 (program): a(n) = 3*n + 2.
• A016790 (program): a(n) = (3n+2)^2.
• A016791 (program): a(n) = (3*n + 2)^3.
• A016792 (program): a(n) = (3*n+2)^4.
• A016793 (program): a(n) = (3*n + 2)^5.
• A016794 (program): a(n) = (3*n + 2)^6.
• A016795 (program): a(n) = (3n+2)^7.
• A016796 (program): a(n) = (3*n + 2)^8.
• A016797 (program): a(n) = (3*n + 2)^9.
• A016798 (program): a(n) = (3*n + 2)^10.
• A016799 (program): a(n) = (3*n + 2)^11.
• A016800 (program): a(n) = (3*n + 2)^12.
• A016801 (program): Expansion of 1/((1-3x)(1-4x)(1-7x)).
• A016802 (program): a(n) = (4*n)^2.
• A016803 (program): (4n)^3.
• A016804 (program): a(n) = (4*n)^4.
• A016805 (program): (4n)^5.
• A016806 (program): a(n) = (4n)^6.
• A016807 (program): a(n) = (4*n)^7.
• A016808 (program): a(n) = (4n)^8.
• A016809 (program): (4n)^9.
• A016810 (program): (4n)^10.
• A016811 (program): (4n)^11.
• A016812 (program): (4n)^12.
• A016813 (program): a(n) = 4*n + 1.
• A016814 (program): a(n) = (4n+1)^2.
• A016815 (program): (4n+1)^3.
• A016816 (program): a(n) = (4n+1)^4.
• A016817 (program): a(n) = (4n+1)^5.
• A016818 (program): (4n+1)^6.
• A016819 (program): a(n) = (4n+1)^7.
• A016820 (program): a(n) = (4*n + 1)^8.
• A016821 (program): a(n) = (4n+1)^9.
• A016822 (program): a(n) = (4n+1)^10.
• A016823 (program): a(n) = (4n+1)^11.
• A016824 (program): (4n+1)^12.
• A016825 (program): Positive integers congruent to 2 (mod 4): a(n) = 4*n+2, for n >= 0.
• A016826 (program): a(n) = (4n + 2)^2.
• A016827 (program): a(n) = (4n+2)^3.
• A016828 (program): a(n) = (4*n+2)^4.
• A016829 (program): (4n+2)^5.
• A016830 (program): a(n) = (4*n+2)^6.
• A016831 (program): (4n+2)^7.
• A016832 (program): a(n) = (4*n + 2)^8.
• A016833 (program): (4n+2)^9.
• A016834 (program): (4n+2)^10.
• A016835 (program): (4n+2)^11.
• A016836 (program): (4n+2)^12.
• A016838 (program): a(n) = (4n + 3)^2.
• A016839 (program): a(n) = (4*n+3)^3.
• A016840 (program): (4n+3)^4.
• A016841 (program): (4n+3)^5.
• A016842 (program): (4n+3)^6.
• A016843 (program): (4n+3)^7.
• A016844 (program): (4n+3)^8.
• A016845 (program): (4n+3)^9.
• A016846 (program): a(n) = (4*n + 3)^10.
• A016847 (program): (4n+3)^11.
• A016848 (program): a(n) = (4*n+3)^12.
• A016849 (program): Expansion of 1/((1-3x)(1-4x)(1-8x)).
• A016850 (program): a(n) = (5*n)^2.
• A016851 (program): a(n) = (5*n)^3.
• A016852 (program): (5n)^4.
• A016853 (program): a(n) = (5*n)^5.
• A016854 (program): a(n) = (5*n)^6.
• A016855 (program): a(n) = (5*n)^7.
• A016856 (program): a(n) = (5*n)^8.
• A016857 (program): a(n) = (5n)^9.
• A016858 (program): (5n)^10.
• A016859 (program): (5n)^11.
• A016860 (program): (5n)^12.
• A016861 (program): a(n) = 5*n + 1.
• A016862 (program): a(n) = (5*n + 1)^2.
• A016863 (program): a(n) = (5*n + 1)^3.
• A016864 (program): a(n) = (5*n + 1)^4.
• A016865 (program): (5n+1)^5.
• A016866 (program): (5n+1)^6.
• A016867 (program): (5n+1)^7.
• A016868 (program): (5n+1)^8.
• A016869 (program): (5n+1)^9.
• A016870 (program): (5n+1)^10.
• A016871 (program): (5n+1)^11.
• A016872 (program): (5n+1)^12.
• A016873 (program): a(n) = 5*n + 2.
• A016874 (program): a(n) = (5*n + 2)^2.
• A016875 (program): (5n+2)^3.
• A016876 (program): (5n+2)^4.
• A016877 (program): a(n) = (5n+2)^5.
• A016878 (program): (5n+2)^6.
• A016879 (program): (5n+2)^7.
• A016880 (program): a(n) = (5*n+2)^8.
• A016881 (program): (5n+2)^9.
• A016882 (program): (5n+2)^10.
• A016883 (program): (5n+2)^11.
• A016884 (program): (5n+2)^12.
• A016885 (program): a(n) = 5*n + 3.
• A016886 (program): a(n) = (5*n + 3)^2.
• A016887 (program): a(n) = (5*n+3)^3.
• A016888 (program): (5n+3)^4.
• A016889 (program): (5n+3)^5.
• A016890 (program): (5n+3)^6.
• A016891 (program): (5n+3)^7.
• A016892 (program): (5n+3)^8.
• A016893 (program): (5n+3)^9.
• A016894 (program): (5n+3)^10.
• A016895 (program): (5n+3)^11.
• A016896 (program): a(n) = (5*n + 3)^12.
• A016897 (program): a(n) = 5n + 4.
• A016898 (program): a(n) = (5*n + 4)^2.
• A016899 (program): a(n) = (5n + 4)^3.
• A016900 (program): a(n) = (5*n + 4)^4.
• A016901 (program): a(n) = (5*n + 4)^5.
• A016902 (program): a(n) = (5*n + 4)^6.
• A016903 (program): a(n) = (5*n + 4)^7.
• A016904 (program): a(n) = (5*n + 4)^8.
• A016905 (program): a(n) = (5*n + 4)^9.
• A016906 (program): a(n) = (5*n + 4)^10.
• A016907 (program): (5n+4)^11.
• A016908 (program): a(n) = (5*n + 4)^12.
• A016909 (program): Expansion of 1/((1-3x)(1-4x)(1-9x)).
• A016910 (program): a(n) = (6*n)^2.
• A016911 (program): a(n) = (6*n)^3.
• A016912 (program): (6n)^4.
• A016913 (program): a(n) = (6*n)^5.
• A016914 (program): a(n) = (6*n)^6.
• A016915 (program): a(n) = (6*n)^7.
• A016916 (program): a(n) = (6n)^8.
• A016917 (program): a(n) = (6*n)^9.
• A016918 (program): a(n) = (6*n)^10.
• A016919 (program): a(n) = (6*n)^11.
• A016920 (program): a(n) = (6*n)^12.
• A016921 (program): a(n) = 6*n + 1.
• A016922 (program): a(n) = (6*n+1)^2.
• A016923 (program): a(n) = (6*n + 1)^3.
• A016924 (program): a(n) = (6*n + 1)^4.
• A016925 (program): a(n) = (6*n + 1)^5.
• A016926 (program): a(n) = (6*n + 1)^6.
• A016927 (program): a(n) = (6*n + 1)^7.
• A016928 (program): a(n) = (6*n + 1)^8.
• A016929 (program): a(n) = (6*n + 1)^9.
• A016930 (program): a(n) = (6*n + 1)^10.
• A016931 (program): a(n) = (6*n + 1)^11.
• A016932 (program): a(n) = (6*n + 1)^12.
• A016933 (program): a(n) = 6n + 2.
• A016934 (program): a(n) = (6*n + 2)^2.
• A016935 (program): a(n) = (6*n + 2)^3.
• A016936 (program): a(n) = (6*n + 2)^4.
• A016937 (program): a(n) = (6*n + 2)^5.
• A016938 (program): a(n) = (6*n + 2)^6.
• A016939 (program): a(n) = (6n+2)^7.
• A016940 (program): a(n) = (6*n + 2)^8.
• A016941 (program): a(n) = (6*n + 2)^9.
• A016942 (program): a(n) = (6*n + 2)^10.
• A016943 (program): a(n) = (6*n + 2)^11.
• A016944 (program): a(n) = (6*n + 2)^12.
• A016945 (program): a(n) = 6*n+3.
• A016946 (program): a(n) = (6*n+3)^2.
• A016947 (program): a(n) = (6*n + 3)^3.
• A016948 (program): a(n) = (6*n + 3)^4.
• A016949 (program): a(n) = (6*n + 3)^5.
• A016950 (program): a(n) = (6*n + 3)^6.
• A016951 (program): a(n) = (6*n + 3)^7.
• A016952 (program): a(n) = (6*n + 3)^8.
• A016953 (program): a(n) = (6*n + 3)^9.
• A016954 (program): a(n) = (6n+3)^10.
• A016955 (program): a(n) = (6*n + 3)^11.
• A016956 (program): a(n) = (6*n + 3)^12.
• A016957 (program): a(n) = 6*n + 4.
• A016958 (program): a(n) = (6n + 4)^2.
• A016959 (program): a(n) = (6*n + 4)^3.
• A016960 (program): a(n) = (6*n + 4)^4.
• A016961 (program): a(n) = (6*n + 4)^5.
• A016962 (program): a(n) = (6*n + 4)^6.
• A016963 (program): a(n) = (6*n + 4)^7.
• A016964 (program): a(n) = (6*n + 4)^8.
• A016965 (program): a(n) = (6*n + 4)^9.
• A016966 (program): a(n) = (6*n + 4)^10.
• A016967 (program): a(n) = (6*n + 4)^11.
• A016968 (program): a(n) = (6*n + 4)^12.
• A016969 (program): a(n) = 6*n + 5.
• A016970 (program): a(n) = (6*n + 5)^2.
• A016971 (program): a(n) = (6*n + 5)^3.
• A016972 (program): a(n) = (6*n + 5)^4.
• A016973 (program): a(n) = (6*n + 5)^5.
• A016974 (program): a(n) = (6*n + 5)^6.
• A016975 (program): a(n) = (6*n + 5)^7.
• A016976 (program): a(n) = (6*n + 5)^8.
• A016977 (program): a(n) = (6*n + 5)^9.
• A016978 (program): a(n) = (6*n + 5)^10.
• A016979 (program): a(n) = (6*n + 5)^11.
• A016980 (program): a(n) = (6*n + 5)^12.
• A016981 (program): Expansion of 1/((1-3x)(1-4x)(1-10x)).
• A016982 (program): a(n) = (7*n)^2.
• A016983 (program): a(n) = (7*n)^3.
• A016984 (program): a(n) = (7*n)^4.
• A016985 (program): a(n) = (7n)^5.
• A016986 (program): a(n) = (7*n)^6.
• A016987 (program): a(n) = (7*n)^7.
• A016988 (program): a(n) = (7*n)^8.
• A016989 (program): a(n) = (7*n)^9.
• A016990 (program): a(n) = (7*n)^10.
• A016991 (program): a(n) = (7*n)^11.
• A016992 (program): a(n) = (7*n)^12.
• A016993 (program): a(n) = 7*n + 1.
• A016994 (program): (7*n+1)^2.
• A016995 (program): a(n) = (7*n + 1)^3.
• A016996 (program): a(n) = (7*n + 1)^4.
• A016997 (program): a(n) = (7*n + 1)^5.
• A016998 (program): a(n) = (7*n + 1)^6.
• A016999 (program): a(n) = (7*n + 1)^7.
• A017000 (program): a(n) = (7*n + 1)^8.
• A017001 (program): a(n) = (7*n + 1)^9.
• A017002 (program): a(n) = (7*n + 1)^10.
• A017003 (program): a(n) = (7*n + 1)^11.
• A017004 (program): a(n) = (7*n + 1)^12.
• A017005 (program): a(n) = 7n + 2.
• A017006 (program): a(n) = (7*n+2)^2.
• A017007 (program): a(n) = (7*n + 2)^3.
• A017008 (program): a(n) = (7*n + 2)^4.
• A017009 (program): a(n) = (7*n + 2)^5.
• A017010 (program): a(n) = (7*n+2)^6.
• A017011 (program): a(n) = (7*n + 2)^7.
• A017012 (program): a(n) = (7*n + 2)^8.
• A017013 (program): a(n) = (7*n + 2)^9.
• A017014 (program): a(n) = (7*n + 2)^10.
• A017015 (program): a(n) = (7*n + 2)^11.
• A017016 (program): a(n) = (7*n + 2)^12.
• A017017 (program): a(n) = 7n+3.
• A017018 (program): a(n) = (7*n + 3)^2.
• A017019 (program): a(n) = (7*n + 3)^3.
• A017020 (program): a(n) = (7*n + 3)^4.
• A017021 (program): a(n) = (7*n + 3)^5.
• A017022 (program): a(n) = (7*n + 3)^6.
• A017023 (program): a(n) = (7*n + 3)^7.
• A017024 (program): a(n) = (7*n + 3)^8.
• A017025 (program): a(n) = (7*n + 3)^9.
• A017026 (program): a(n) = (7*n + 3)^10.
• A017027 (program): a(n) = (7*n + 3)^11.
• A017028 (program): a(n) = (7*n + 3)^12.
• A017029 (program): a(n) = 7*n + 4.
• A017030 (program): a(n) = (7*n + 4)^2.
• A017031 (program): a(n) = (7*n + 4)^3.
• A017032 (program): a(n) = (7*n + 4)^4.
• A017033 (program): a(n) = (7*n + 4)^5.
• A017034 (program): a(n) = (7*n + 4)^6.
• A017035 (program): a(n) = (7*n + 4)^7.
• A017036 (program): (7*n+4)^8.
• A017037 (program): a(n) = (7*n + 4)^9.
• A017038 (program): a(n) = (7*n + 4)^10.
• A017039 (program): a(n) = (7*n + 4)^11.
• A017040 (program): a(n) = (7*n