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A322800 Number of compositions (ordered partitions) of n into octagonal numbers (A000567). 4
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 (list; graph; refs; listen; history; text; internal format)
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 A107322 A050761

Adjacent sequences:  A322797 A322798 A322799 * A322801 A322802 A322803

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2018

STATUS

approved

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Last modified March 31 16:44 EDT 2020. Contains 333151 sequences. (Running on oeis4.)