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A319400
Number of partitions of n into exactly seven positive Fibonacci numbers.
4
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, 21, 24, 22, 27, 25, 27, 26, 31, 28, 30, 29, 32, 29, 32, 30, 34, 33, 34, 34, 37, 36, 38, 36, 41, 37, 38, 39, 41, 41, 40, 39, 41, 38, 41, 38, 41, 42, 40, 41, 46, 43
OFFSET
0,10
LINKS
FORMULA
a(n) = [x^n y^7] 1/Product_{j>=2} (1-y*x^A000045(j)).
MAPLE
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))(7):
seq(a(n), n=0..120);
CROSSREFS
Column k=7 of A319394.
Cf. A000045.
Sequence in context: A348588 A106247 A337030 * A174787 A094909 A237799
KEYWORD
nonn,look
AUTHOR
Alois P. Heinz, Sep 18 2018
STATUS
approved