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%I #6 Dec 28 2018 20:34:59
%S 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,
%T 126,156,195,244,304,377,466,575,709,874,1080,1338,1660,2061,2557,
%U 3170,3926,4857,6006,7428,9191,11380,14096,17465,21640,26807,33197,41099
%N Number of compositions (ordered partitions) of n into octagonal numbers (A000567).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=1} x^(k*(3*k-2))).
%p h:= proc(n) option remember; `if`(n<1, 0, (t->
%p `if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
%p end:
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(n-i*(3*i-2)), i=1..h(n)))
%p end:
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Dec 28 2018
%t nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (3 k - 2)), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000567, A006456, A023361, A181324, A279041, A279281, A322798, A322799.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Dec 26 2018
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