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A319399 Number of partitions of n into exactly six positive Fibonacci numbers.

%I A319399 #6 Oct 05 2020 11:09:51
%S A319399 0,0,0,0,0,0,1,1,2,2,4,4,6,6,8,8,9,9,12,10,12,12,14,13,15,13,16,15,16,
%T A319399 15,19,16,18,18,20,18,20,17,20,17,19,19,21,21,20,20,24,21,23,21,23,22,
%U A319399 22,23,24,23,23,20,22,21,20,21,24,22,22,23,25,25,27,23
%N A319399 Number of partitions of n into exactly six positive Fibonacci numbers.
%H A319399 Alois P. Heinz, <a href="/A319399/b319399.txt">Table of n, a(n) for n = 0..17711</a>
%F A319399 a(n) = [x^n y^6] 1/Product_{j>=2} (1-y*x^A000045(j)).
%p A319399 h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
%p A319399       issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
%p A319399     end:
%p A319399 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
%p A319399       t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319399     end:
%p A319399 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(6):
%p A319399 seq(a(n), n=0..120);
%Y A319399 Column k=6 of A319394.
%Y A319399 Cf. A000045.
%K A319399 nonn,look
%O A319399 0,9
%A A319399 _Alois P. Heinz_, Sep 18 2018