A066351 Bisection of A007059.

1, 2, 5, 14, 43, 140, 472, 1628, 5719, 20388, 73562, 268066, 984911, 3643570, 13557020, 50691978, 190353370, 717457656, 2713061899, 10289600164, 39127877886, 149147692734, 569767908076, 2180978471298, 8363866011929, 32129445138352, 123618810558184

Offset

0,2

References

R. Kemp, Balanced ordered trees, Random Structures and Algorithms, 5, 1994, 99-121.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

Conjecture: a(n) ~ 0.721... * 4^n / n. - Vaclav Kotesovec, Aug 25 2014

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      `if`(m=0, add(b(n-j, j), j=1..n),
      add(b(n-j, min(n-j, m)), j=1..min(n, m))))
    end:
a:= n-> b(2*n, 0):
seq(a(n), n=0..40);  # Alois P. Heinz, May 13 2014

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, 1, If[m == 0, Sum[b[n - j, j], {j, 1, n} ], Sum[b[n - j, Min[n - j, m]], {j, 1, Min[n, m]}]]]; a[n_] := b[2*n, 0]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *)

Crossrefs

Sequence in context: A366025 A366042 A149880 * A181496 A276989 A272461

Adjacent sequences: A066348 A066349 A066350 * A066352 A066353 A066354

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 19 2001

Extensions

More terms from Emeric Deutsch, Jun 10 2004

Status

approved