A322800 Number of compositions (ordered partitions) of n into octagonal numbers (A000567).

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 37, 46, 56, 68, 83, 102, 126, 156, 195, 244, 304, 377, 466, 575, 709, 874, 1080, 1338, 1660, 2061, 2557, 3170, 3926, 4857, 6006, 7428, 9191, 11380, 14096, 17465, 21640, 26807, 33197, 41099

Offset

0,9

Links

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

Eric Weisstein's World of Mathematics, Octagonal Number

Index entries for sequences related to compositions

Formula

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

Maple

h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(3*i-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^(k (3 k - 2)), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000567, A006456, A023361, A181324, A279041, A279281, A322798, A322799.

Sequence in context: A023358 A322855 A322803 * A061379 A050761 A030721

Adjacent sequences: A322797 A322798 A322799 * A322801 A322802 A322803

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved