A303170 Number of ordered ways of writing n as a sum of n tetrahedral numbers.

1, 1, 1, 1, 5, 21, 61, 141, 309, 757, 2111, 6051, 16721, 44617, 118301, 318501, 871781, 2400741, 6596953, 18067329, 49460555, 135697395, 373271515, 1028451579, 2835353337, 7819016521, 21572619771, 59562583471, 164586609409, 455114644297, 1259191262441, 3485551053561

Offset: 0

Author

Ilya Gutkovskiy, Apr 19 2018

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index to sequences related to pyramidal numbers

Crossrefs

Main diagonal of A290429.

Cf. A000292, A068980, A106337, A282582, A303172.

Programs

Mathematica

Table[SeriesCoefficient[Sum[x^(k (k + 1) (k + 2)/6), {k, 0, n}]^n, {x, 0, n}], {n, 0, 31}]

Formula

a(n) = [x^n] (Sum_{k>=0} x^(k*(k+1)*(k+2)/6))^n.

a(n) = A290429(n,n).