OFFSET
0,5
COMMENTS
Number of partitions of n into centered triangular numbers (A005448).
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's World of Mathematics, Centered Triangular Number
FORMULA
G.f.: Product_{k>=0} 1/(1 - x^(3*k*(k+1)/2+1)).
EXAMPLE
a(8) = 3 because we have [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
MAPLE
N:= 100:
kmax:= floor((sqrt(24*N-15)-3)/6):
S:= series(mul(1/(1-x^(3*k*(k+1)/2+1)), k=0..kmax), x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Jan 25 2017
MATHEMATICA
nmax = 78; CoefficientList[Series[Product[1/(1 - x^(3 k (k + 1)/2 + 1)), {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 11 2017
STATUS
approved