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

%I A322801 #8 Feb 16 2025 08:33:57
%S A322801 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,
%T A322801 363,468,605,784,1017,1320,1712,2217,2869,3713,4807,6227,8070,10458,
%U A322801 13549,17549,22726,29430,38117,49375,63962,82859,107333,139026,180071
%N A322801 Number of compositions (ordered partitions) of n into centered pentagonal numbers (A005891).
%H A322801 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPentagonalNumber.html">Centered Pentagonal Number</a>
%H A322801 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A322801 G.f.: 1/(1 - Sum_{k>=0} x^(5*k*(k+1)/2+1)).
%p A322801 h:= proc(n) option remember; `if`(n<0, 0, (t->
%p A322801       `if`(((t+1)*5*t+2)/2>n, t-1, t))(1+h(n-1)))
%p A322801     end:
%p A322801 a:= proc(n) option remember; `if`(n=0, 1,
%p A322801       add(a(n-((i+1)*5*i+2)/2), i=0..h(n)))
%p A322801     end:
%p A322801 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018
%t A322801 nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(5 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]
%Y A322801 Cf. A005891, A181324, A280863, A280952, A281083, A282502, A282504, A322802, A322803.
%K A322801 nonn
%O A322801 0,7
%A A322801 _Ilya Gutkovskiy_, Dec 26 2018