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A322798 Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).

%I A322798 #10 Feb 16 2025 08:33:57
%S A322798 1,1,1,1,1,1,2,3,4,5,6,7,9,12,16,22,29,37,47,60,77,101,133,174,226,
%T A322798 292,376,486,632,823,1072,1394,1808,2342,3036,3939,5116,6648,8636,
%U A322798 11211,14548,18875,24493,31795,41283,53604,69594,90338,117251,152184,197540
%N A322798 Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).
%H A322798 Alois P. Heinz, <a href="/A322798/b322798.txt">Table of n, a(n) for n = 0..8828</a>
%H A322798 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>
%H A322798 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A322798 G.f.: 1/(1 - Sum_{k>=1} x^(k*(2*k-1))).
%p A322798 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A322798       `if`(t*(2*t-1)>n, t-1, t))(1+h(n-1)))
%p A322798     end:
%p A322798 a:= proc(n) option remember; `if`(n=0, 1,
%p A322798       add(a(n-i*(2*i-1)), i=1..h(n)))
%p A322798     end:
%p A322798 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018
%t A322798 nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A322798 Cf. A000384, A006456, A023361, A181324, A278949, A279279, A322799, A322800.
%K A322798 nonn
%O A322798 0,7
%A A322798 _Ilya Gutkovskiy_, Dec 26 2018