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

Author

Stan Wagon, Nov 06 2015

Keywords

• easy
• nonn

Examples

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

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

Crossrefs

Cf. A006946, A135831, A135907.

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

Programs

Mathematica

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

PARI

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

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