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A006788
a(n) = floor(2^(n-1)/n).
(Formerly M0712)
5
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
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
Sequence in context: A000048 A056303 A074099 * A054650 A022857 A000691
KEYWORD
nonn
STATUS
approved