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A319818 Number of partitions of n into exactly eight positive triangular numbers.

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