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A289203
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Number of maximum independent vertex sets in the n X n knight graph.
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2
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1, 1, 2, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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For n > 4, a(n) = ((-1)^n + 3)/2.
G.f.: (x*(-1 - x - x^2 - 5*x^3 + x^4 + 4*x^5))/(-1 + x^2).
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MATHEMATICA
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Table[Length[With[{g = KnightTourGraph[n, n]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]]], {n, 8}]
Table[Piecewise[{{1, n == 2}, {2, n == 3}, {6, n == 4}, {2, Mod[n, 2] == 0}, {1, Mod[n, 2] == 1}}], {n, 100}]
Table[Piecewise[{{1, n == 2}, {2, n == 3}, {6, n == 4}}, ((-1)^n + 3)/2], {n, 100}]
CoefficientList[Series[(-1 - x - x^2 - 5 x^3 + x^4 + 4 x^5)/(-1 + x^2), {x, 0, 20}], x]
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PROG
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(Python)
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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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STATUS
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approved
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