Sequences

Euler transform of 5 4 3 2 1 1 1 1 1 1 1 ...

Expansion of q^(5/24) / (eta(q) * eta(q^2)^2) in powers of q.

Expansion of Product_{k >= 1} 1/(1-x^k)^c(k), where c(1), c(2), ... = 2 3 2 3 2 3 2 3 ....

G:=1/product((1-x^(3k-2))*(1-x^(3k-1))^2*(1-x^(3k))^3,k=1..infinity).

Smallest covering radius of [ n,6 ] binary code.

Size of minimal binary covering code of length n and covering radius 2.

Size of minimal covering code with 1 ternary coordinate and n binary coordinates, with covering radius 1.

Number of connected functions on n points with a loop of length 5.

Number of connected functions on n points with a loop of length 6.

Number of connected functions on n points with a loop of length 7.

Number of connected functions on n points with a loop of length 8.

Low temperature series for spin-1/2 Ising specific heat on 2D square lattice.

Low temperature series for spin-1/2 Ising specific heat on 2D square lattice, multiplied by 4.

Low temperature series for spin-1/2 Ising specific heat on 2D square lattice, divided by 8.

Related to a bound for Giuga's conjecture.

Number of Giuga sequences of length n.

Euler transform of Thue-Morse sequence A001285.

Inverse Euler transform of {A001285(0), A001285(1), ...} where A001285(n) is Thue-Morse sequence.

Binomial transform of Thue-Morse sequence A001285.

Inverse binomial transform of Thue-Morse sequence A001285.

Möbius transform of Thue-Morse sequence A001285 (when shifted once right).

Inverse Moebius transform of Thue-Morse sequence A001285.

First differences of Thue-Morse sequence A001285.

Second differences of Thue-Morse sequence A001285.

Boustrophedon transform of 1 followed by Thue-Morse sequence A001285.

Convolution of Thue-Morse sequence A001285 with itself.

A sum over scaled A000531 related to Catalan numbers C(n).

Convolution of Thue-Morse sequence A001285 with primes.

Number of graphical partitions (degree-vectors for graphs with n vertices, allowing self-loops which count as degree 1; or possible ordered row-sum vectors for a symmetric 0-1 matrix).

Number of odd graphical partitions.

Number of even graphical partitions.

Number of even graphical partitions of order 2n - number of odd graphical partitions of order 2n.

Number of graphical partitions with up to n parts (?).

Number of directed (or Gale-Ryser) graphical partitions: degree-vector pairs (in-degree, out-degree) for directed graphs (loops allowed) with n vertices; or possible ordered pair (row-sum, column-sum) vectors for a 0-1 matrix.

Number of partitions of floor(n^2/2) with at most n parts and maximal height n.

Convolution of Thue-Morse sequence A001285 with A008578 = {1, primes}.

Theta series of 13-dimensional lattice Kappa_13 with minimal norm 4.

Pitoun's sequence: a(n+1) is digital root of a(0) + ... + a(n).

Number of strategic configurations in 3 X n Chomp rectangle.

f(n) where strategic move on f(n) X 3 rectangle in Chomp is (n,1).

g(n), where strategic move on g(n) X 3 rectangle in Chomp is (h(n),2).

h(n), where strategic move on g(n) X 3 rectangle in Chomp is (h(n),2). Conjectured to be complementary to r(n), see A029905.

p(n), where exists one-parameter family of strategic partitions (k+p(n)+q(n), k+q(n), r(n)) for k = 0,1,2,... in Chomp.

q(n), where exists one-parameter family of strategic partitions (k+p(n)+q(n), k+q(n), r(n)) for k = 0,1,2,... in Chomp.

r(n), where exists one-parameter family of strategic partitions (k+p(n)+q(n), k+q(n), r(n)) for k = 0,1,2,... in Chomp.

Zack's sequence (the pattern is evident).

a(n+1) = a(n) + a(n-1) + Fibonacci(n), with a(0) = 0 and a(1) = 1.

Starting with n, repeatedly sum prime factors (with multiplicity) until reaching 0 or a fixed point. Then a(n) is the fixed point (or 0).

Starting with n (but omitting the primes), repeatedly sum prime factors (counted with multiplicity) until reaching a limit.

Start with n; if prime, stop; repeatedly sum prime factors (counted with multiplicity) and add 1, until reach 1, 6 or a prime.