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A226254 - OEIS
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A226254
Number of ways of writing n as the sum of 10 triangular numbers from A000217.
16
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
0,2
LINKS
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.
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
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: A226450 A105938 A342254 * A340966 A022605 A211032
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 01 2013
STATUS
approved