A286911 Number of edge covers in the ladder graph P_2 x P_n.

1, 7, 43, 277, 1777, 11407, 73219, 469981, 3016729, 19363879, 124293499, 797819173, 5121067777, 32871277183, 210995228083, 1354343064493, 8693301516841, 55800847838359, 358176305451691, 2299073773191541, 14757369859827601, 94725087867636847

Offset: 1

Author

Andrew Howroyd, May 15 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, Ladder Graph
• Index entries for linear recurrences with constant coefficients, signature (6, 3, -2).

Crossrefs

Row 2 of A286912.

Cf. A123304, A020866.

Programs

Mathematica

Table[-RootSum[2 - 3 # - 6 #^2 + #^3 &, -14 #^n - 5 #^(n + 1) + #^(n + 2) &]/30, {n, 20}] (* Eric W. Weisstein, Aug 09 2017 *)
LinearRecurrence[{6, 3, -2}, {1, 7, 43}, 20] (* Eric W. Weisstein, Aug 09 2017 *)
CoefficientList[Series[(1 + x - 2 x^2)/(1 - 6 x - 3 x^2 + 2 x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 09 2017 *)

Formula

a(n) = 6*a(n-1) + 3*a(n-2) - 2*a(n-3) for n > 3.

G.f.: x*(1-x)*(1+2*x)/(1-6*x-3*x^2+2*x^3).