A322856 Number of compositions (ordered partitions) of n into octagonal pyramidal numbers (A002414).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 54, 64, 76, 91, 110, 135, 166, 204, 250, 305, 370, 447, 539, 650, 787, 956, 1164, 1419, 1730, 2107, 2562, 3110, 3770, 4569, 5540, 6723, 8166, 9926, 12070, 14677, 17841, 21675

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A002414, A279224, A280863, A282582, A322340, A322800, A322853, A322854, A322855.

Programs

Mathematica

nmax = 56; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k - 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

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