A322802 Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 36, 45, 56, 70, 88, 111, 140, 178, 226, 286, 361, 455, 573, 721, 909, 1148, 1451, 1834, 2318, 2928, 3695, 4661, 5880, 7420, 9366, 11826, 14935, 18860, 23812, 30059, 37941, 47888, 60445, 76302, 96327

Offset

0,8

Links

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

Eric Weisstein's World of Mathematics, Hex Number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=0} x^(3*k*(k+1)+1)).

Maple

h:= proc(n) option remember; `if`(n<0, 0, (t->
      `if`(3*t*(t+1)+1>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-(3*i*(i+1)+1)), i=0..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018

Mathematica

nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(3 k (k + 1) + 1), {k, 0, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A003215, A280863, A280953, A281084, A282502, A282504, A322798, A322801, A322803.

Sequence in context: A017901 A101917 A322854 * A322799 A218550 A127273

Adjacent sequences: A322799 A322800 A322801 * A322803 A322804 A322805

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved