A284700 Number of edge covers in the n-antiprism graph.

4, 13, 205, 2902, 41413, 590758, 8427370, 120219259, 1714968133, 24464596729, 348995693650, 4978540849669, 71020558255594, 1013132129923498, 14452670295681235, 206172198577335937, 2941115696724530533, 41956003773586931038, 598516493115066264085

Offset

0,1

Comments

Sequence extrapolated to n=0 using recurrence. - Andrew Howroyd, May 15 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..860 (terms 0..200 from Andrew Howroyd)

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Edge Cover

Index entries for linear recurrences with constant coefficients, signature (13,18,1,-4).

Formula

From Andrew Howroyd, May 15 2017 (Start)

a(n) = 13*a(n-1)+18*a(n-2)+a(n-3)-4*a(n-4) for n>=4.

G.f.: (-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1).

(End)

Mathematica

Table[RootSum[4 - # - 18 #^2 - 13 #^3 + #^4 &, #^n &], {n, 0, 20}] (* Eric W. Weisstein, May 17 2017 *)
LinearRecurrence[{13, 18, 1, -4}, {13, 205, 2902, 41413}, {0, 20}] (* Eric W. Weisstein, May 17 2017 *)
CoefficientList[Series[(-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1), {x, 0, 50}], x]

Prog

(PARI)
Vec((-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1)+O(x^20)) \\ Andrew Howroyd, May 15 2017

Crossrefs

Cf. A123304, A020866, A192742, A286910, A284699.

Sequence in context: A220038 A132512 A203221 * A050629 A348140 A376025

Adjacent sequences: A284697 A284698 A284699 * A284701 A284702 A284703

Keyword

nonn

Author

Eric W. Weisstein, Apr 01 2017

Extensions

a(0)-a(2) and a(9)-a(18) from Andrew Howroyd, May 15 2017

Status

approved