OFFSET
0,2
COMMENTS
Number of ways of writing n as the sum of 24 triangular numbers from A000217.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
J. G. Huard and K. S. Williams, Sums of sixteen and twenty-four triangular numbers, Rocky Mountain J. Math. Volume 35, Number 3 (2005), 857-868.
K. Ono, S. Robins and P. T. Wahl, On the representation of integers as sums of triangular numbers, Aequationes mathematicae, August 1995, Volume 50, Issue 1-2, pp 73-94. Case k=24, Theorem 8.
FORMULA
From Wolfdieter Lang, Jan 13 2017: (Start)
G.f.: 24th power of the g.f. for A010054.
a(n) = (A096963(n+3) - tau(n+3) - 2072*tau((n+3)/2))/176896, with Ramanujan's tau function given in A000594, and tau(n) is put to 0 if n is not integer. See the Ono et al. link, case k=24, Theorem 8.
(End)
a(n) = 1/72 * Sum_{a, b, x, y > 0, a*x + b*y = n + 3, x == y == 1 mod 2 and a > b} (a*b)^3*(a^2 - b^2)^2. - Seiichi Manyama, May 05 2017
a(0) = 1, a(n) = (24/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017
G.f.: exp(Sum_{k>=1} 24*(x^k/k)/(1 + x^k)). - Ilya Gutkovskiy, Jul 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Seiichi Manyama, May 05 2017
STATUS
approved