A006788 a(n) = floor(2^(n-1)/n).

1, 1, 1, 2, 3, 5, 9, 16, 28, 51, 93, 170, 315, 585, 1092, 2048, 3855, 7281, 13797, 26214, 49932, 95325, 182361, 349525, 671088, 1290555, 2485513, 4793490, 9256395, 17895697, 34636833, 67108864, 130150524, 252645135, 490853405, 954437176, 1857283155, 3616814565

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Very close to A000048. [Fisher, 1989]

This is the number of nested polygons needed to produce a graph that is always concave, see the MathWorld article. - Jon Perry, Sep 15 2002

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• H. L. Fisher, Letter to N. J. A. Sloane, Mar 16 1989
• Simon Michalowsky, Bahman Gharesifard and Christian Ebenbauer, A Lie bracket approximation approach to distributed optimization over directed graphs, arXiv:1711.05486 [math.OC], 2017.
• Eric Weisstein's World of Mathematics, Happy End Problem

Crossrefs

Cf. A054650, A000048.

Programs

Magma

[Floor(2^(n-1)/n) : n in [1..40]]; // Vincenzo Librandi, Sep 24 2011

Mathematica

Table[Quotient[2^n, 2*n], {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)

Python

print([2**(n-1)//n for n in range(1, 40)]) # Gennady Eremin, Feb 04 2022

Sage

A006788 = lambda n: (1<A006788(n) for n in (1..38)] # Peter Luschny, Sep 18 2014