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 A289203 Number of maximum independent vertex sets in the n X n knight graph. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Eric Weisstein's World of Mathematics, Independent Vertex Set Eric Weisstein's World of Mathematics, Knight Graph Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set Index entries for linear recurrences with constant coefficients, signature (0, 1). FORMULA 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). MATHEMATICA 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] CROSSREFS Cf. A000034. Sequence in context: A126749 A024573 A191359 * A246505 A302551 A078434 Adjacent sequences:  A289200 A289201 A289202 * A289204 A289205 A289206 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jun 28 2017 STATUS approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)