A288029 Number of minimal edge covers in the ladder graph P_2 X P_n.

1, 2, 6, 17, 45, 120, 324, 873, 2349, 6322, 17018, 45809, 123305, 331904, 893400, 2404801, 6473097, 17423890, 46900574, 126244129, 339816309, 914696984, 2462126012, 6627401865, 17839239445, 48018585634, 129253524146, 347916817697, 936501444241, 2520817938240

Offset: 1

Author

Andrew Howroyd, Jun 04 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Ladder Graph
• Eric Weisstein's World of Mathematics, Minimal Edge Cover
• Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, 1, 0, -1).

Crossrefs

Row 2 of A288025.

Cf. A288030, A288027.

Programs

Mathematica

Table[(RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, 94 #^n + 33 #^(n + 1) - 7 #^(n + 2) + 8 #^(n + 3) &] + 182 (2 Cos[n Pi/2] + Sin[n Pi/2]))/910, {n, 20}] (* Eric W. Weisstein, Aug 03 2017 *)
LinearRecurrence[{2, 1, 2, 1, 0, -1}, {1, 2, 6, 17, 45, 120}, 20] (* Eric W. Weisstein, Aug 03 2017 *)
CoefficientList[Series[(1 + x^2 + x^3 - x^5)/(1 - 2 x - x^2 - 2 x^3 - x^4 + x^6), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 03 2017 *)

PARI

Vec((1+x^2+x^3-x^5)/((1+x^2)*(1-2*x-2*x^2+x^4))+O(x^20))

Formula

a(n) = 2*a(n-1)+a(n-2)+2*a(n-3)+a(n-4)-a(n-6) for n>6.

G.f.: x*(1+x^2+x^3-x^5)/((1+x^2)*(1-2*x-2*x^2+x^4)).