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

1,2

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, Edge Cover

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, 1, 0, -1).

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)).

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 *)

Prog

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

Crossrefs

Row 2 of A288025.

Cf. A288030, A288027.

Sequence in context: A020963 A065068 A109961 * A268655 A350431 A316591

Adjacent sequences: A288026 A288027 A288028 * A288030 A288031 A288032

Keyword

nonn

Author

Andrew Howroyd, Jun 04 2017

Status

approved