cp's OEIS Frontend

A319403 Number of partitions of n into exactly ten positive Fibonacci numbers.

%I A319403 #6 Oct 05 2020 11:11:39
%S A319403 0,0,0,0,0,0,0,0,0,0,1,1,2,2,4,4,6,7,10,11,14,15,19,20,24,25,31,30,35,
%T A319403 36,42,42,48,47,54,54,59,60,69,66,73,72,80,79,86,85,92,91,97,96,107,
%U A319403 103,110,110,118,117,123,123,132,130,135,134,142,141,146,145
%N A319403 Number of partitions of n into exactly ten positive Fibonacci numbers.
%H A319403 Alois P. Heinz, <a href="/A319403/b319403.txt">Table of n, a(n) for n = 0..17711</a>
%F A319403 a(n) = [x^n y^10] 1/Product_{j>=2} (1-y*x^A000045(j)).
%p A319403 h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
%p A319403       issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
%p A319403     end:
%p A319403 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
%p A319403       t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319403     end:
%p A319403 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(10):
%p A319403 seq(a(n), n=0..120);
%Y A319403 Column k=10 of A319394.
%Y A319403 Cf. A000045.
%K A319403 nonn,look
%O A319403 0,13
%A A319403 _Alois P. Heinz_, Sep 18 2018