A341072 Number of compositions of 2n into n Fibonacci parts.

1, 1, 3, 7, 23, 71, 231, 750, 2479, 8251, 27673, 93248, 315515, 1071097, 3646618, 12445982, 42571327, 145895599, 500855361, 1722062265, 5929045173, 20439121983, 70539320558, 243695962031, 842704577995, 2916613479471, 10102511916071, 35018749192885

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A121548(2n,n).

a(n) ~ c * d^n / sqrt(n), where d = 3.532272846853808150678856189005437981671101510837727... and c = 0.2903295565097076269212760734928134309226027... - Vaclav Kotesovec, Feb 14 2021

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, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(g(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..35);

Mathematica

g[n_] := g[n] = With[{t = 5*n^2}, IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4]];
b[n_, t_] := b[n, t] =
     If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
     If[g[j], b[n - j, t - 1], 0], {j, 1, n}]]];
a[n_] := b[2n, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 02 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000045, A121548, A341071.

Sequence in context: A151454 A106936 A088704 * A148702 A194691 A148703

Adjacent sequences: A341069 A341070 A341071 * A341073 A341074 A341075

Keyword

nonn

Author

Alois P. Heinz, Feb 04 2021

Status

approved