A322799 Number of compositions (ordered partitions) of n into heptagonal numbers (A000566).

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 29, 37, 46, 57, 71, 89, 112, 143, 183, 233, 295, 372, 468, 588, 741, 937, 1188, 1506, 1908, 2414, 3049, 3848, 4857, 6136, 7757, 9812, 12414, 15702, 19852, 25089, 31703, 40061, 50631, 64004, 80923, 102318

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..9828

Eric Weisstein's World of Mathematics, Heptagonal Number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(5*k-3)/2)).

Maple

h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(5*t-3)/2>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(5*i-3)/2), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018

Mathematica

nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (5 k - 3)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000566, A006456, A023361, A181324, A279012, A279280, A322798, A322800.

Sequence in context: A101917 A322854 A322802 * A218550 A127273 A143287

Adjacent sequences: A322796 A322797 A322798 * A322800 A322801 A322802

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved