A322854 Number of compositions (ordered partitions) of n into hexagonal pyramidal numbers (A002412).

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 35, 43, 53, 67, 85, 108, 137, 173, 217, 271, 340, 428, 540, 682, 861, 1085, 1364, 1714, 2155, 2712, 3416, 4305, 5425, 6832, 8599, 10821, 13618, 17142, 21584, 27182, 34231, 43102, 54264, 68311, 85994

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A002412, A279222, A282582, A322340, A322798, A322802, A322853, A322855, A322856.

Programs

Mathematica

nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (4 k - 1)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(4*k-1)/6)).