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A202604
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Clique number for the n-Keller graph.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.).
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LINKS
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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.
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from N. J. A. Sloane, Jul 04 2017 based on the Jarnicki et al. survey.
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STATUS
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approved
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