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

0,10

Links

Table of n, a(n) for n=0..56.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index entries for sequences related to compositions

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A130224 A017903 A005711 * A280863 A059765 A180479

Adjacent sequences: A322853 A322854 A322855 * A322857 A322858 A322859

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2018

Status

approved