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A322802 Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).

%I A322802 #8 Feb 16 2025 08:33:57
%S A322802 1,1,1,1,1,1,1,2,3,4,5,6,7,8,10,13,17,22,28,36,45,56,70,88,111,140,
%T A322802 178,226,286,361,455,573,721,909,1148,1451,1834,2318,2928,3695,4661,
%U A322802 5880,7420,9366,11826,14935,18860,23812,30059,37941,47888,60445,76302,96327
%N A322802 Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).
%H A322802 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexNumber.html">Hex Number</a>
%H A322802 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A322802 G.f.: 1/(1 - Sum_{k>=0} x^(3*k*(k+1)+1)).
%p A322802 h:= proc(n) option remember; `if`(n<0, 0, (t->
%p A322802       `if`(3*t*(t+1)+1>n, t-1, t))(1+h(n-1)))
%p A322802     end:
%p A322802 a:= proc(n) option remember; `if`(n=0, 1,
%p A322802       add(a(n-(3*i*(i+1)+1)), i=0..h(n)))
%p A322802     end:
%p A322802 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018
%t A322802 nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(3 k (k + 1) + 1), {k, 0, nmax}]), {x, 0, nmax}], x]
%Y A322802 Cf. A003215, A280863, A280953, A281084, A282502, A282504, A322798, A322801, A322803.
%K A322802 nonn
%O A322802 0,8
%A A322802 _Ilya Gutkovskiy_, Dec 26 2018