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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

Table of n, a(n) for n=1..92.

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.)