A322855 Number of compositions (ordered partitions) of n into heptagonal pyramidal numbers (A002413).

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 97, 121, 151, 188, 233, 287, 352, 431, 530, 654, 809, 1002, 1241, 1535, 1895, 2335, 2876, 3544, 4371, 5396, 6666, 8237, 10176, 12564, 15504, 19126, 23594, 29111, 35928

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A002413, A279223, A282582, A322340, A322799, A322803, A322853, A322854, A322856.

Programs

Mathematica

nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (5 k - 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(5*k-2)/6)).