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A319400 Number of partitions of n into exactly seven positive Fibonacci numbers.

%I A319400 #6 Oct 05 2020 11:10:24
%S A319400 0,0,0,0,0,0,0,1,1,2,2,4,4,6,7,9,9,11,11,14,14,16,15,19,17,20,20,22,
%T A319400 21,24,22,27,25,27,26,31,28,30,29,32,29,32,30,34,33,34,34,37,36,38,36,
%U A319400 41,37,38,39,41,41,40,39,41,38,41,38,41,42,40,41,46,43
%N A319400 Number of partitions of n into exactly seven positive Fibonacci numbers.
%H A319400 Alois P. Heinz, <a href="/A319400/b319400.txt">Table of n, a(n) for n = 0..17711</a>
%F A319400 a(n) = [x^n y^7] 1/Product_{j>=2} (1-y*x^A000045(j)).
%p A319400 h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
%p A319400       issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
%p A319400     end:
%p A319400 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
%p A319400       t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319400     end:
%p A319400 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(7):
%p A319400 seq(a(n), n=0..120);
%Y A319400 Column k=7 of A319394.
%Y A319400 Cf. A000045.
%K A319400 nonn,look
%O A319400 0,10
%A A319400 _Alois P. Heinz_, Sep 18 2018