A319397 Number of partitions of n into exactly four positive Fibonacci numbers.

0, 0, 0, 0, 1, 1, 2, 2, 4, 3, 4, 4, 5, 4, 5, 4, 5, 5, 5, 5, 7, 4, 5, 4, 5, 5, 6, 5, 6, 5, 6, 5, 7, 4, 4, 3, 5, 5, 4, 6, 6, 5, 6, 4, 6, 6, 5, 5, 5, 5, 5, 4, 7, 4, 1, 4, 2, 4, 6, 3, 6, 5, 5, 6, 5, 6, 5, 3, 6, 3, 5, 6, 5, 6, 5, 2, 5, 3, 6, 5, 2, 5, 4, 3, 7, 1, 4

Offset

0,7

Links

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

Formula

a(n) = [x^n y^4] 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))(4):
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 = 4}, b[n, h[n], k] - b[n, h[n], k - 1]];
a /@ Range[0, 120] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A319394.

Cf. A000045.

Sequence in context: A357978 A087808 A217754 * A094950 A087874 A363341

Adjacent sequences: A319394 A319395 A319396 * A319398 A319399 A319400

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2018

Status

approved