A226252 Number of ways of writing n as the sum of 7 triangular numbers.

1, 7, 21, 42, 77, 126, 175, 253, 357, 434, 567, 735, 833, 1057, 1302, 1400, 1708, 2037, 2191, 2597, 3003, 3151, 3619, 4242, 4389, 4935, 5691, 5740, 6594, 7434, 7371, 8400, 9303, 9506, 10626, 11592, 11585, 12761, 14427, 14203, 15519, 17241, 16808, 18788, 20559, 19950, 21882, 23898, 23786

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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.

Formula

G.f. is 7th power of g.f. for A010054.

a(0) = 1, a(n) = (7/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017

G.f.: exp(Sum_{k>=1} 7*(x^k/k)/(1 + x^k)). - Ilya Gutkovskiy, Jul 31 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/32) * exp(7*Pi/8) * Pi^(7/4) * 2^(5/8) / Gamma(3/4)^7 = A388793. - Simon Plouffe, Sep 18 2025

Crossrefs

Number of ways of writing n as a sum of k triangular numbers, for k=1,...: A010054, A008441, A008443, A008438, A008439, A008440, A226252, A007331, A226253, A226254, A226255, A014787, A014809.

Sequence in context: A162818 A024966 A342250 * A340963 A022602 A054569

Adjacent sequences: A226249 A226250 A226251 * A226253 A226254 A226255

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2013

Status

approved