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A322799 Number of compositions (ordered partitions) of n into heptagonal numbers (A000566).

%I A322799 #10 Feb 16 2025 08:33:57
%S A322799 1,1,1,1,1,1,1,2,3,4,5,6,7,8,10,13,17,22,29,37,46,57,71,89,112,143,
%T A322799 183,233,295,372,468,588,741,937,1188,1506,1908,2414,3049,3848,4857,
%U A322799 6136,7757,9812,12414,15702,19852,25089,31703,40061,50631,64004,80923,102318
%N A322799 Number of compositions (ordered partitions) of n into heptagonal numbers (A000566).
%H A322799 Alois P. Heinz, <a href="/A322799/b322799.txt">Table of n, a(n) for n = 0..9828</a>
%H A322799 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>
%H A322799 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A322799 G.f.: 1/(1 - Sum_{k>=1} x^(k*(5*k-3)/2)).
%p A322799 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A322799       `if`(t*(5*t-3)/2>n, t-1, t))(1+h(n-1)))
%p A322799     end:
%p A322799 a:= proc(n) option remember; `if`(n=0, 1,
%p A322799       add(a(n-i*(5*i-3)/2), i=1..h(n)))
%p A322799     end:
%p A322799 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018
%t A322799 nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (5 k - 3)/2), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A322799 Cf. A000566, A006456, A023361, A181324, A279012, A279280, A322798, A322800.
%K A322799 nonn
%O A322799 0,8
%A A322799 _Ilya Gutkovskiy_, Dec 26 2018