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Alois P. Heinz, <a href="/A319399/b319399.txt">Table of n, a(n) for n = 0..17711</a>

allocated for Alois P. Heinz

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

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, 15, 19, 16, 18, 18, 20, 18, 20, 17, 20, 17, 19, 19, 21, 21, 20, 20, 24, 21, 23, 21, 23, 22, 22, 23, 24, 23, 23, 20, 22, 21, 20, 21, 24, 22, 22, 23, 25, 25, 27, 23

0,9

a(n) = [x^n y^6] 1/Product_{j>=2} (1-y*x^A000045(j)).

h:= proc(n) option remember; `if`(n<1, 0, `if`((t->

issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))

end:

b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or

t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))

end:

a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(6):

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

Column k=6 of A319394.

Cf. A000045.

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Alois P. Heinz, Sep 18 2018

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