A359515 Number of compositions (ordered partitions) of n into at most 3 positive Fibonacci numbers (with a single type of 1).

1, 1, 2, 4, 6, 9, 10, 11, 12, 12, 12, 14, 12, 12, 11, 12, 15, 12, 14, 12, 6, 12, 8, 14, 15, 9, 15, 12, 9, 14, 6, 12, 6, 0, 12, 8, 11, 17, 9, 15, 9, 6, 15, 9, 12, 9, 0, 14, 6, 6, 12, 0, 6, 0, 0, 12, 8, 11, 14, 9, 17, 9, 6, 15, 6, 9, 6, 0, 15, 9, 9, 12, 0, 9, 0, 0, 14, 6, 6, 6, 0, 12

Offset

0,3

Links

Table of n, a(n) for n=0..81.

Formula

a(n) = Sum_{k=0..3} 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, 3):
seq(a(n), n=0..81);  # Alois P. Heinz, Jan 03 2023

Mathematica

g[n_] := With[{t = 5 n^2}, IntegerQ @ Sqrt[t+4] || IntegerQ @ Sqrt[t-4]];
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, 3];
Table[a[n], {n, 0, 81}] (* Jean-François Alcover, May 28 2023, after Alois P. Heinz *)

Crossrefs

Cf. A000045, A076739, A121548, A121550, A359512, A359514, A359516.

Sequence in context: A114526 A333387 A178126 * A162202 A210380 A228359

Adjacent sequences: A359512 A359513 A359514 * A359516 A359517 A359518

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 03 2023

Status

approved