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A319402 Number of partitions of n into exactly nine positive Fibonacci numbers.

%I A319402 #6 Oct 05 2020 11:05:46
%S A319402 0,0,0,0,0,0,0,0,0,1,1,2,2,4,4,6,7,10,11,13,14,18,18,22,23,27,26,31,
%T A319402 30,36,36,39,39,45,43,49,49,55,52,58,56,63,62,65,64,71,68,73,72,79,77,
%U A319402 82,81,87,86,90,89,96,93,96,96,101,100,101,100,107,103,108
%N A319402 Number of partitions of n into exactly nine positive Fibonacci numbers.
%H A319402 Alois P. Heinz, <a href="/A319402/b319402.txt">Table of n, a(n) for n = 0..17711</a>
%F A319402 a(n) = [x^n y^9] 1/Product_{j>=2} (1-y*x^A000045(j)).
%p A319402 h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
%p A319402       issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
%p A319402     end:
%p A319402 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
%p A319402       t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319402     end:
%p A319402 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(9):
%p A319402 seq(a(n), n=0..120);
%Y A319402 Column k=9 of A319394.
%Y A319402 Cf. A000045.
%K A319402 nonn,look
%O A319402 0,12
%A A319402 _Alois P. Heinz_, Sep 18 2018