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A134041 a(n) = number of binary partitions of the Fibonacci number F(n). 1
1, 2, 2, 4, 6, 14, 36, 114, 450, 2268, 14442, 118686, 1264678, 17519842, 318273566, 7607402556, 240151303078, 10055927801538, 559859566727028, 41582482495661986, 4129785050606801246, 549628445573614296188, 98256218721544814784486, 23631541930531250077261282 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A276057 A116637 A153961 * A358366 A069925 A357951
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 02 2007
STATUS
approved

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Last modified June 24 23:28 EDT 2024. Contains 373691 sequences. (Running on oeis4.)