A226253 Number of ways of writing n as the sum of 9 triangular numbers.

1, 9, 36, 93, 198, 378, 633, 990, 1521, 2173, 2979, 4113, 5370, 6858, 8955, 11055, 13446, 16830, 20031, 23724, 28836, 33381, 38520, 45729, 52203, 59121, 68922, 77461, 86283, 99747, 110547, 121500, 138870, 152034, 166725, 188568, 204156, 221760, 248310, 268713, 289422, 321786, 345570, 369036

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 9th power of g.f. for A010054.

a(0) = 1, a(n) = (9/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017

G.f.: exp(Sum_{k>=1} 9*(x^k/k)/(1 + x^k)). - Ilya Gutkovskiy, Jul 31 2017

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: A162258 A128642 A342252 * A340965 A022604 A085630

Adjacent sequences: A226250 A226251 A226252 * A226254 A226255 A226256

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2013

Status

approved