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

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]]

Prog

(PARI) a(n)=if(n>2, 2^n, n+3) \\ Charles R Greathouse IV, Nov 07 2015

Crossrefs

Cf. A006946, A135831, A135907.

Essentially the same as A143858, A240951, A198633, A171497, A151821, A146541 and A077552.

Sequence in context: A145265 A244161 A362959 * A275929 A240794 A171938

Adjacent sequences: A258932 A258933 A258934 * A258936 A258937 A258938

Keyword

easy,nonn

Author

Stan Wagon, Nov 06 2015

Status

approved