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A319395
Number of partitions of n into exactly two positive Fibonacci numbers.
5
0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,5
LINKS
FORMULA
a(n) = [x^n y^2] 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))(2):
seq(a(n), n=0..120);
MATHEMATICA
h[n_] := h[n] = If[n < 1, 0, If[Function[t, IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 4]][5 n^2], n, h[n - 1]]];
b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i < 1 || t < 1, 0, b[n, h[i - 1], t] + b[n - i, h[Min[n - i, i]], t - 1]]];
a[n_] := With[{k = 2}, b[n, h[n], k] - b[n, h[n], k - 1]];
a /@ Range[0, 120] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A319394.
Cf. A000045.
Sequence in context: A257886 A144477 A106345 * A374462 A194636 A286299
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 18 2018
STATUS
approved