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%I #6 Oct 05 2020 11:11:03
%S 0,0,0,0,0,0,0,0,1,1,2,2,4,4,6,7,10,10,12,13,16,16,20,19,23,22,25,25,
%T 30,28,31,31,35,34,39,36,42,40,43,42,47,44,47,46,51,48,52,51,56,55,57,
%U 56,62,59,62,60,65,64,64,65,67,64,67,65,70,67,69,68,72
%N Number of partitions of n into exactly eight positive Fibonacci numbers.
%H Alois P. Heinz, <a href="/A319401/b319401.txt">Table of n, a(n) for n = 0..17711</a>
%F a(n) = [x^n y^8] 1/Product_{j>=2} (1-y*x^A000045(j)).
%p h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
%p issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
%p end:
%p b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
%p t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p end:
%p a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(8):
%p seq(a(n), n=0..120);
%Y Column k=8 of A319394.
%Y Cf. A000045.
%K nonn,look
%O 0,11
%A _Alois P. Heinz_, Sep 18 2018
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