A359514 Number of compositions (ordered partitions) of n into at most 2 positive Fibonacci numbers (with a single type of 1).

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Formula

a(n) = Sum_{k=0..2} A121548(n,k). - Alois P. Heinz, Jan 03 2023

Maple

g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
b:= proc(n, t) option remember; `if`(n=0, 1, `if`(t<1, 0,
      add(`if`(g(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 2):
seq(a(n), n=0..94);  # Alois P. Heinz, Jan 03 2023

Mathematica

g[n_] := IntegerQ@Sqrt[# + 4] || IntegerQ@Sqrt[# - 4]&[5 n^2];
b[n_, t_] := b[n, t] = If[n == 0, 1, If[t < 1, 0, Sum[If[g[j], b[n - j, t - 1], 0], {j, 1, n}]]];
a[n_] := b[n, 2];
Table[a[n], {n, 0, 94}] (* Jean-François Alcover, May 26 2023, after Alois P. Heinz *)

Crossrefs

Cf. A000045, A076739, A121548, A121549, A359511, A359515, A359516.

Sequence in context: A350857 A135715 A089326 * A237367 A022923 A276858

Adjacent sequences: A359511 A359512 A359513 * A359515 A359516 A359517

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 03 2023

Status

approved