A226254 Number of ways of writing n as the sum of 10 triangular numbers from A000217.

1, 10, 45, 130, 300, 612, 1105, 1830, 2925, 4420, 6341, 9000, 12325, 16290, 21645, 27932, 34980, 44370, 54900, 66430, 81702, 98050, 115440, 138330, 162565, 187800, 220545, 254800, 289265, 334890, 382058, 427350, 488700, 550420, 609960, 691812, 770185, 845750, 949365, 1049400, 1145580, 1274580

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. Case k=10, Theorem 6.

Crossrefs

Cf. A000217, A030212, A050456.

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 10th power of g.f. for A010054.

a(n) = (A050456(4*n+5) - A030212(4*n+5))/640. See the Ono et al. link, case k=10, Theorem 6. - Wolfdieter Lang, Jan 13 2017

a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - Seiichi Manyama, May 06 2017

G.f.: exp(Sum_{k>=1} 10*(x^k/k)/(1 + x^k)). - Ilya Gutkovskiy, Jul 31 2017