A319398 Number of partitions of n into exactly five positive Fibonacci numbers.

0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 5, 5, 7, 6, 7, 7, 8, 7, 9, 8, 10, 9, 9, 8, 11, 8, 10, 10, 11, 10, 11, 10, 13, 10, 11, 8, 10, 10, 10, 11, 12, 11, 11, 11, 13, 11, 12, 11, 12, 12, 11, 11, 13, 12, 10, 8, 10, 9, 9, 12, 11, 10, 13, 10, 14, 14, 11, 11, 11, 11, 13

Offset

0,8

Links

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

Formula

a(n) = [x^n y^5] 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))(5):
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 = 5}, b[n, h[n], k] - b[n, h[n], k - 1]];
a /@ Range[0, 120] (* Jean-François Alcover, Dec 08 2020 *)

Crossrefs

Column k=5 of A319394.

Cf. A000045.

Sequence in context: A116648 A152850 A036714 * A260734 A265428 A035644

Adjacent sequences: A319395 A319396 A319397 * A319399 A319400 A319401

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2018

Status

approved