A134041 a(n) = number of binary partitions of the Fibonacci number F(n).

1, 2, 2, 4, 6, 14, 36, 114, 450, 2268, 14442, 118686, 1264678, 17519842, 318273566, 7607402556, 240151303078, 10055927801538, 559859566727028, 41582482495661986, 4129785050606801246, 549628445573614296188, 98256218721544814784486, 23631541930531250077261282

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..125

Formula

a(n) = A000123( A000045(n) ) for n>=0.

Maple

g:= proc(b, n) option remember; local t; if b<0 then 0 elif b=0 or n=0 then 1 elif b>=n then add(g(b-t, n) *binomial(n+1, t) *(-1)^(t+1), t=1..n+1) else g(b-1, n) +g(2*b, n-1) fi end: f:= proc(n) local t; t:= ilog2(2*n+1); g(n/2^(t-1), t) end: a:= n-> f(combinat[fibonacci](n)): seq(a(n), n=0..25);  # Alois P. Heinz, Sep 26 2011

Mathematica

g[b_, n_] := g[b, n] = If[b < 0, 0, If[b == 0 || n == 0, 1, If[b >= n, Sum[g[b - t, n] Binomial[n + 1, t] (-1)^(t + 1), {t, 1, n + 1}], g[b - 1, n] + g[2b, n - 1]]]];
f[n_] := With[{t = Floor@Log[2, 2n + 1]}, g[n/2^(t - 1), t]];
a[n_] := f[Fibonacci[n]];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000123, A000045.

Sequence in context: A276057 A116637 A153961 * A358366 A069925 A357951

Adjacent sequences: A134038 A134039 A134040 * A134042 A134043 A134044

Keyword

nonn

Author

Paul D. Hanna, Oct 02 2007

Status

approved