OFFSET
1,5
COMMENTS
a(n) gives the number of times n occurs in A225794. - Antti Karttunen, Jul 27 2013
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Brian Hopkins, Michael A. Jones, Shift-Induced Dynamical Systems on Partitions and Compositions, Electron. J. Combin. 13 (2006), Research Paper 80.
Brian Hopkins and James A. Sellers, Exact enumeration of Garden of Eden partitions, INTEGERS: Electronic Journal of Combinatorial Number Theory 7(2) (2007), #A19.
FORMULA
a(n) = Sum_{j>=1} (-1)^(j+1)*p(n-b(j)) where b(j) = 3*j*(j+1)/2 (A045943) and p(n) is the number of partitions of n (see A000041). See Hopkins & Sellers. - Michel Marcus, Sep 26 2018
a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)) * (1 - (1/(2*Pi) + 19*Pi/144) / sqrt(n/6)). - Vaclav Kotesovec, May 26 2023
MAPLE
p:=product(1/(1-q^i), i=1..200)*sum((-1)^(r-1)*q^((3*r^2+3*r)/2), r=1..200):s:=series(p, q, 200): for j from 0 to 199 do printf(`%d, `, coeff(s, q, j)) od: # James A. Sellers, Nov 30 2006
PROG
(PARI) my(N=50, x='x+O('x^N)); concat([0, 0], Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(3*k*(k+1)/2)))) \\ Seiichi Manyama, May 21 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Nov 23 2006
EXTENSIONS
More terms from James A. Sellers, Nov 30 2006
STATUS
approved