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A319816 Number of partitions of n into exactly six positive triangular numbers.

%I A319816 #4 Sep 28 2018 11:12:37
%S A319816 1,0,1,0,1,1,1,1,1,2,2,2,2,2,3,3,3,2,4,4,5,3,5,4,6,6,4,7,6,8,7,7,7,8,
%T A319816 10,7,10,10,10,10,11,10,12,13,12,13,14,14,14,16,14,16,16,14,20,19,18,
%U A319816 17,21,18,22,21,20,22,26,23,21,25,24,29,26,23,29,30
%N A319816 Number of partitions of n into exactly six positive triangular numbers.
%H A319816 Alois P. Heinz, <a href="/A319816/b319816.txt">Table of n, a(n) for n = 6..10000</a>
%F A319816 a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^A000217(j)).
%p A319816 h:= proc(n) option remember; `if`(n<1, 0,
%p A319816       `if`(issqr(8*n+1), n, h(n-1)))
%p A319816     end:
%p A319816 b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
%p A319816       k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
%p A319816     end:
%p A319816 a:= n-> b(n, h(n), 6):
%p A319816 seq(a(n), n=6..120);
%Y A319816 Column k=6 of A319797.
%Y A319816 Cf. A000217.
%K A319816 nonn
%O A319816 6,10
%A A319816 _Alois P. Heinz_, Sep 28 2018