A319816 - OEIS

%I #4 Sep 28 2018 11:12:37

%S 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 10,7,10,10,10,10,11,10,12,13,12,13,14,14,14,16,14,16,16,14,20,19,18,

%U 17,21,18,22,21,20,22,26,23,21,25,24,29,26,23,29,30

%N Number of partitions of n into exactly six positive triangular numbers.

%H Alois P. Heinz, <a href="/A319816/b319816.txt">Table of n, a(n) for n = 6..10000</a>

%F a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^A000217(j)).

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

%p       `if`(issqr(8*n+1), n, h(n-1)))

%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(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))

%p     end:

%p a:= n-> b(n, h(n), 6):

%p seq(a(n), n=6..120);

%Y Column k=6 of A319797.

%Y Cf. A000217.

%K nonn

%O 6,10

%A _Alois P. Heinz_, Sep 28 2018