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

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

• nonn

Links

• Wikipedia, Centered heptagonal number
• Index entries for sequences related to compositions

Crossrefs

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

Programs

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]

Formula

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