A287225 -id:A287225 - cp's OEIS frontend

A289202 Number of maximum matchings in the n X n knight graph.

1, 1, 2, 16, 644, 10304, 65113608, 2849759680, 118928612871184, 58888109421793792

Offset: 1

Eric W. Weisstein, Jun 28 2017

Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Knight Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set

Join[{1, 1}, Table[Length[With[{g = LineGraph[KnightTourGraph[n, n]]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]]], {n, 3, 5}]]

a(7)-a(10) from Andrew Howroyd, Jul 01 2017

A302241 Triangle T(n,k) read by rows giving the coefficients of the matching-generating polynomial of the n X n knight graph (0 <= k <= floor(n^2/2)).

Original entry on oeis.org

1, 1, 1, 8, 20, 16, 2, 1, 24, 224, 1032, 2464, 2944, 1592, 320, 16, 1, 48, 964, 10592, 70024, 289344, 754244, 1226288, 1203410, 670000, 189544, 22112, 644, 1, 80, 2828, 58432, 786982, 7298848, 48033800, 227891056, 784428297, 1956801264, 3509779148, 4458911088, 3919123796, 2301829920, 858287984, 187915392, 21263600, 980608, 10304

Offset: 1

Eric W. Weisstein, Apr 03 2018

			Rows as polynomials:
1,
1,
1 + 8*x + 20*x^2 + 16*x^3 + 2*x^4,
1 + 24*x + 224*x^2 + 1032*x^3 + 2464*x^4 + 2944*x^5 + 1592*x^6 + 320*x^7 + 16*x^8,
1 + 48*x + 964*x^2 + 10592*x^3 + 70024*x^4 + 289344*x^5 + 754244*x^6 + 1226288*x^7 + 1203410*x^8 + 670000*x^9 + 189544*x^10 + 22112*x^11 + 644*x^12,
...

Eric Weisstein's World of Mathematics, Knight Graph
Eric Weisstein's World of Mathematics, Matching-Generating Polynomial

Row sums are A287225.

cp's OEIS Frontend

A289202 Number of maximum matchings in the n X n knight graph.

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