A282582 Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292).

1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 15, 21, 29, 40, 57, 81, 114, 159, 223, 314, 444, 625, 878, 1233, 1736, 2445, 3441, 4838, 6804, 9573, 13473, 18957, 26668, 37514, 52780, 74264, 104488, 147000, 206808, 290961, 409369, 575955, 810314, 1140029, 1603924, 2256603, 3174867, 4466763, 6284339, 8841533, 12439323

Offset: 0

Author

Ilya Gutkovskiy, Feb 19 2017

Keywords

• nonn

Examples

			a(8) = 7 because we have [4, 4], [4, 1, 1, 1, 1], [1, 4, 1, 1, 1], [1, 1, 4, 1, 1], [1, 1, 1, 4, 1], [1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..100
• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index to sequences related to pyramidal numbers
• Index entries for sequences related to compositions

Crossrefs

Cf. A000292, A023361, A068980, A279278, A282172.

Programs

Mathematica

nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (k + 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

Vec(1/(1 - sum(k=1, 50, x^(k*(k + 1)*(k + 2)/6)) + O(x^51))) \\ Indranil Ghosh, Mar 15 2017

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(k+2)/6)).