A006788 a(n) = floor(2^(n-1)/n). (Formerly M0712)

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

1,4

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

Mathematica

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

Prog

(Magma) [Floor(2^(n-1)/n) : n in [1..40]]; // Vincenzo Librandi, Sep 24 2011
(Sage)
A006788 = lambda n: (1<<n)//(2*n)
[A006788(n) for n in (1..38)] # Peter Luschny, Sep 18 2014
(Python)
print([2**(n-1)//n for n in range(1, 40)]) # Gennady Eremin, Feb 04 2022

Crossrefs

Cf. A054650, A000048.

Sequence in context: A000048 A056303 A074099 * A054650 A022857 A000691

Adjacent sequences: A006785 A006786 A006787 * A006789 A006790 A006791

Keyword

nonn

Author

N. J. A. Sloane

Status

approved