A319400 - OEIS

%I #6 Oct 05 2020 11:10:24

%S 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 21,24,22,27,25,27,26,31,28,30,29,32,29,32,30,34,33,34,34,37,36,38,36,

%U 41,37,38,39,41,41,40,39,41,38,41,38,41,42,40,41,46,43

%N Number of partitions of n into exactly seven positive Fibonacci numbers.

%H Alois P. Heinz, <a href="/A319400/b319400.txt">Table of n, a(n) for n = 0..17711</a>

%F a(n) = [x^n y^7] 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))(7):

%p seq(a(n), n=0..120);

%Y Column k=7 of A319394.

%Y Cf. A000045.

%K nonn,look

%O 0,10

%A _Alois P. Heinz_, Sep 18 2018