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%I #6 Dec 28 2018 20:35:50
%S 1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,11,14,18,23,29,36,45,55,67,82,101,
%T 125,155,192,239,297,368,455,562,694,857,1058,1308,1619,2005,2483,
%U 3074,3805,4708,5822,7198,8900,11007,13616,16846,20845,25795,31918,39489
%N Number of compositions (ordered partitions) of n into centered heptagonal numbers (A069099).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Centered_heptagonal_number">Centered heptagonal number</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=0} x^(7*k*(k+1)/2+1)).
%p h:= proc(n) option remember; `if`(n<1, 0, (t->
%p `if`((7*(t-1)*t+2)/2>n, t-1, t))(1+h(n-1)))
%p end:
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(n-(7*(i-1)*i+2)/2), i=1..h(n)))
%p end:
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Dec 28 2018
%t nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(7 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]
%Y Cf. A069099, A280863, A282502, A282504, A322799, A322801, A322802.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Dec 26 2018
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