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A319401
Number of partitions of n into exactly eight positive Fibonacci numbers.
4
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 10, 12, 13, 16, 16, 20, 19, 23, 22, 25, 25, 30, 28, 31, 31, 35, 34, 39, 36, 42, 40, 43, 42, 47, 44, 47, 46, 51, 48, 52, 51, 56, 55, 57, 56, 62, 59, 62, 60, 65, 64, 64, 65, 67, 64, 67, 65, 70, 67, 69, 68, 72
OFFSET
0,11
LINKS
FORMULA
a(n) = [x^n y^8] 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))(8):
seq(a(n), n=0..120);
CROSSREFS
Column k=8 of A319394.
Cf. A000045.
Sequence in context: A094909 A237799 A318029 * A322369 A319402 A319403
KEYWORD
nonn,look
AUTHOR
Alois P. Heinz, Sep 18 2018
STATUS
approved