%I #4 Sep 28 2018 11:19:35
%S 1,0,1,0,1,1,1,1,1,2,2,2,2,2,4,3,4,3,4,5,6,4,6,6,7,7,7,8,9,11,9,10,11,
%T 11,14,13,13,15,16,15,18,18,18,19,22,20,22,25,23,27,26,26,29,29,32,32,
%U 36,31,37,39,37,39,42,41,47,48,44,48,52,52,54,55,55
%N Number of partitions of n into exactly eight positive triangular numbers.
%H Alois P. Heinz, <a href="/A319818/b319818.txt">Table of n, a(n) for n = 8..10000</a>
%F a(n) = [x^n y^8] 1/Product_{j>=1} (1y*x^A000217(j)).
%p h:= proc(n) option remember; `if`(n<1, 0,
%p `if`(issqr(8*n+1), n, h(n1)))
%p end:
%p b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
%p k>n or i*k<n, 0, b(n, h(i1), k)+b(ni, h(min(ni, i)), k1)))
%p end:
%p a:= n> b(n, h(n), 8):
%p seq(a(n), n=8..120);
%Y Column k=8 of A319797.
%Y Cf. A000217.
%K nonn
%O 8,10
%A _Alois P. Heinz_, Sep 28 2018
