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

Author

N. J. A. Sloane, Jun 01 2013

Keywords

• nonn

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.

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.

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