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A258935
Independence number of Keller graphs.
2
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
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
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]]
PROG
(PARI) a(n)=if(n>2, 2^n, n+3) \\ Charles R Greathouse IV, Nov 07 2015
CROSSREFS
Essentially the same as A143858, A240951, A198633, A171497, A151821, A146541 and A077552.
Sequence in context: A145265 A244161 A362959 * A275929 A240794 A171938
KEYWORD
easy,nonn
AUTHOR
Stan Wagon, Nov 06 2015
STATUS
approved