A297349 Number of edge covers in the 2 X n king graph.

1, 41, 1201, 36281, 1094401, 33014921, 995960401, 30045123161, 906370788001, 27342474236201, 824840018262001, 24882936703189241, 750643185668251201, 22644641945255809481, 683120580615598976401, 20607688511425541428121, 621671836326816125138401

Offset: 1

Author

Andrew Howroyd, Dec 28 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Edge Cover
• Eric Weisstein's World of Mathematics, King Graph
• Index entries for linear recurrences with constant coefficients, signature (29,36,-24).

Crossrefs

Row 2 of A297205.

Programs

Mathematica

(* Start from Eric W. Weisstein, Dec 29 2017 *)
Table[-RootSum[24 - 36 # - 29 #^2 + #^3 &, -9152 #^n - 1682 #^(n + 1) + 65 #^(n + 2) &]/16889, {n, 20}]
-RootSum[24 - 36 # - 29 #^2 + #^3 &, #^Range[20] (-9152 - 1682 # + 65 #^2) &]/16889
LinearRecurrence[{29, 36, -24}, {1, 41, 1201}, 20]
CoefficientList[Series[(1 + 12 x - 24 x^2)/(1 - 29 x - 36 x^2 + 24 x^3), {x, 0, 20}], x]
(* End *)

PARI

Vec(x*(1 + 12*x - 24*x^2)/(1 - 29*x - 36*x^2 + 24*x^3) + O(x^20))

Formula

a(n) = 29*a(n-1) + 36*a(n-2) - 24*a(n-3) for n > 3.

G.f.: x*(1 + 12*x - 24*x^2)/(1 - 29*x - 36*x^2 + 24*x^3).