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A202604
Clique number for the n-Keller graph.
4
1, 2, 5, 12, 28, 60, 124, 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
1,2
COMMENTS
a(n) <= 2^n.
a(7) = 124 was established by Debroni et al. (2011).
a(8) = 2^8 was established by Mackey (2002).
a(n) = 2^n for n >= 8 (see Jarnicki et al.).
LINKS
J. Debroni, J. D. Eblen, M. A. Langston, P. Shor, W. Myrvold, D. Weerapurage, A complete resolution of the Keller maximum clique problem, Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms, pp. 129-135, 2011.
Witold Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, Proved and Conjectured, of Keller, Mycielski, and Queen Graphs, arXiv preprint arXiv:1606.07918 [math.CO], 2016.
J. Mackey, A cube tiling of dimension eight with no facesharing, Discrete & Computational Geometry 28 (2): 275-279, 2002.
Eric Weisstein's World of Mathematics, Clique Number
Eric Weisstein's World of Mathematics, Keller Graph
FORMULA
G.f.: x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1 - 2*x). - Colin Barker, Oct 14 2017
MATHEMATICA
Table[Piecewise[{{1, n == 1}, {2, n == 2}, {5, n == 3}, {2^n - 4, 4 <= n <= 7}}, 2^n], {n, 20}] (* Eric W. Weisstein, Mar 21 2018 *)
Join[{1, 2, 5, 12, 28, 60, 124}, LinearRecurrence[{2}, {256}, 14]] (* Eric W. Weisstein, Mar 21 2018 *)
CoefficientList[Series[(-1 - x^2 - 2 x^3 - 4 x^4 - 4 x^5 - 4 x^6 - 8 x^7)/(-1 + 2 x), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 21 2018 *)
PROG
(PARI) Vec(x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1 - 2*x) + O(x^40)) \\ Colin Barker, Oct 14 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 21 2011
EXTENSIONS
More terms from N. J. A. Sloane, Jul 04 2017 based on the Jarnicki et al. survey.
STATUS
approved