A319396 Number of partitions of n into exactly three positive Fibonacci numbers.

0, 0, 0, 1, 1, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 1, 2, 1, 3, 3, 2, 2, 3, 2, 3, 1, 3, 1, 0, 2, 1, 2, 3, 2, 3, 2, 1, 2, 2, 3, 2, 0, 3, 1, 1, 3, 0, 1, 0, 0, 2, 1, 2, 2, 2, 3, 2, 1, 3, 1, 2, 1, 0, 2, 2, 2, 3, 0, 2, 0, 0, 3, 1, 1, 1, 0, 3, 0, 0, 1, 0, 0

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..17711

Formula

a(n) = [x^n y^3] 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))(3):
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 = 3}, 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=3 of A319394.

Cf. A000045.

Sequence in context: A255933 A340805 A343556 * A049237 A162361 A171135

Adjacent sequences: A319393 A319394 A319395 * A319397 A319398 A319399

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2018

Status

approved