A319819 - OEIS

%I #4 Sep 28 2018 11:23:35

%S 1,0,1,0,1,1,1,1,1,2,2,2,2,2,4,3,4,3,5,5,6,5,6,6,8,8,7,9,10,11,11,11,

%T 12,13,15,14,16,17,17,19,20,19,23,23,24,25,27,27,28,33,30,33,34,34,41,

%U 39,41,41,46,44,49,50,49,54,59,56,58,63,63,68,70,67

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

%H Alois P. Heinz, <a href="/A319819/b319819.txt">Table of n, a(n) for n = 9..10000</a>

%F a(n) = [x^n y^9] 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), 9):

%p seq(a(n), n=9..120);

%Y Column k=9 of A319797.

%Y Cf. A000217.

%K nonn

%O 9,10

%A _Alois P. Heinz_, Sep 28 2018