A322799 - OEIS

%I #9 Dec 28 2018 20:49:51

%S 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 183,233,295,372,468,588,741,937,1188,1506,1908,2414,3049,3848,4857,

%U 6136,7757,9812,12414,15702,19852,25089,31703,40061,50631,64004,80923,102318

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

%H Alois P. Heinz, <a href="/A322799/b322799.txt">Table of n, a(n) for n = 0..9828</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^(k*(5*k-3)/2)).

%p h:= proc(n) option remember; `if`(n<1, 0, (t->

%p       `if`(t*(5*t-3)/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-i*(5*i-3)/2), i=1..h(n)))

%p     end:

%p seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 28 2018

%t nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (5 k - 3)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A000566, A006456, A023361, A181324, A279012, A279280, A322798, A322800.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Dec 26 2018