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

0,8

Links

Table of n, a(n) for n=0..53.

Eric Weisstein's World of Mathematics, Hexagonal Pyramidal Number

Index entries for sequences related to compositions

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A005709 A017901 A101917 * A322802 A322799 A218550

Adjacent sequences: A322851 A322852 A322853 * A322855 A322856 A322857

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2018

Status

approved