A322801 Number of compositions (ordered partitions) of n into centered pentagonal numbers (A005891).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 28, 36, 46, 59, 76, 98, 128, 167, 217, 281, 363, 468, 605, 784, 1017, 1320, 1712, 2217, 2869, 3713, 4807, 6227, 8070, 10458, 13549, 17549, 22726, 29430, 38117, 49375, 63962, 82859, 107333, 139026, 180071

Offset: 0

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Centered Pentagonal Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A005891, A181324, A280863, A280952, A281083, A282502, A282504, A322802, A322803.

Programs

Maple

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

Mathematica

nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(5 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=0} x^(5*k*(k+1)/2+1)).