A359516 Number of compositions (ordered partitions) of n into at most 4 positive Fibonacci numbers (with a single type of 1).

1, 1, 2, 4, 7, 13, 20, 27, 35, 40, 46, 50, 55, 60, 61, 60, 65, 68, 72, 76, 73, 72, 66, 66, 79, 73, 85, 80, 79, 90, 76, 84, 85, 60, 72, 56, 69, 85, 69, 99, 89, 70, 97, 73, 94, 97, 66, 90, 72, 70, 96, 60, 85, 60, 24, 72, 44, 71, 88, 57, 105, 85, 78, 111, 74, 97, 82, 48, 97, 69, 79

Offset

0,3

Links

Table of n, a(n) for n=0..70.

Formula

a(n) = Sum_{k=0..4} 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, 4):
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 03 2023

Mathematica

g[n_] := Function[t, IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 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, 4];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 13 2023, after Alois P. Heinz *)

Crossrefs

Cf. A000045, A076739, A121548, A357688, A359513, A359514, A359515.

Sequence in context: A162842 A164901 A262744 * A347703 A112997 A037032

Adjacent sequences: A359513 A359514 A359515 * A359517 A359518 A359519

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 03 2023

Status

approved