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

%I A322800 #7 Feb 16 2025 08:33:57
%S A322800 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 A322800 126,156,195,244,304,377,466,575,709,874,1080,1338,1660,2061,2557,
%U A322800 3170,3926,4857,6006,7428,9191,11380,14096,17465,21640,26807,33197,41099
%N A322800 Number of compositions (ordered partitions) of n into octagonal numbers (A000567).
%H A322800 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H A322800 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A322800 G.f.: 1/(1 - Sum_{k>=1} x^(k*(3*k-2))).
%p A322800 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A322800       `if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
%p A322800     end:
%p A322800 a:= proc(n) option remember; `if`(n=0, 1,
%p A322800       add(a(n-i*(3*i-2)), i=1..h(n)))
%p A322800     end:
%p A322800 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018
%t A322800 nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (3 k - 2)), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A322800 Cf. A000567, A006456, A023361, A181324, A279041, A279281, A322798, A322799.
%K A322800 nonn
%O A322800 0,9
%A A322800 _Ilya Gutkovskiy_, Dec 26 2018