A258935 - OEIS

A258935

Independence number of Keller graphs.

4, 5, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

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OFFSET

1,1

REFERENCES

W. Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, proved and conjectured, of Keller, queen, and Mycielski graphs, Ars Mathematica Contemporanea 13:2 (2017) 427-460.

LINKS

Table of n, a(n) for n=1..33.

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

Eric Weisstein's World of Mathematics, Independence Number

Eric Weisstein's World of Mathematics, Keller Graph

FORMULA

a(n) = 2^n except a(1) = 4 and a(2) = 5.

G.f.: x*(x*(3+2*x)-4)/(2*x-1), e.g.f.: exp(2*x)+x^2/2+2*x-1. - Benedict W. J. Irwin, Jul 15 2016

EXAMPLE

For G(2), a maximum independent set is {03,10,12,13,23}.

MATHEMATICA

Join[{4, 5}, 2^Range[3, 10]]