A322803 Number of compositions (ordered partitions) of n into centered heptagonal numbers (A069099).

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 45, 55, 67, 82, 101, 125, 155, 192, 239, 297, 368, 455, 562, 694, 857, 1058, 1308, 1619, 2005, 2483, 3074, 3805, 4708, 5822, 7198, 8900, 11007, 13616, 16846, 20845, 25795, 31918, 39489

Offset

0,9

Links

Table of n, a(n) for n=0..54.

Wikipedia, Centered heptagonal number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=0} x^(7*k*(k+1)/2+1)).

Maple

h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`((7*(t-1)*t+2)/2>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-(7*(i-1)*i+2)/2), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018

Mathematica

nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(7 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A069099, A280863, A282502, A282504, A322799, A322801, A322802.

Sequence in context: A291146 A023358 A322855 * A322800 A061379 A050761

Adjacent sequences: A322800 A322801 A322802 * A322804 A322805 A322806

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved