A287082 Number of edge covers on the n-web graph.

6, 52, 360, 2576, 18336, 130624, 930432, 6627584, 47208960, 336274432, 2395318272, 17062105088, 121535176704, 865707900928, 6166528819200, 43924836122624, 312881247289344, 2228686172717056, 15875167014617088, 113080491469438976

Offset

1,1

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Edge Cover

Eric Weisstein's World of Mathematics, Web Graph

Index entries for linear recurrences with constant coefficients, signature (6,8).

Formula

a(n) = (3-sqrt(17))^n + (3+sqrt(17))^n.

G.f.: -((2*x*(3+8*x))/(-1+6*x+8*x^2)).

a(n) = 6*a(n-1) + 8*a(n-2) for n>2. - Colin Barker, May 20 2017

a(n) = I^n*2^((3*n + 2)/2)*ChebyshevT(n, -3*I/(2*sqrt(2))). - Eric W. Weisstein, Dec 24 2017

Mathematica

Table[(3 - Sqrt[17])^n + (3 + Sqrt[17])^n, {n, 20}] // Expand
LinearRecurrence[{6, 8}, {6, 52}, 20]
CoefficientList[Series[-2 (3 + 8 x)/(-1 + 6 x + 8 x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 24 2017 *)
Table[I^n 2^((3 n + 2)/2) ChebyshevT[n, -3 I/(2 Sqrt[2])], {n, 20}] (* Eric W. Weisstein, Dec 24 2017 *)

Prog

(PARI) Vec(2*x*(3 + 8*x) / (1 - 6*x - 8*x^2) + O(x^30)) \\ Colin Barker, May 20 2017

Crossrefs

Sequence in context: A357428 A292053 A202925 * A007974 A027111 A083301

Adjacent sequences: A287079 A287080 A287081 * A287083 A287084 A287085

Keyword

nonn,easy

Author

Eric W. Weisstein, May 19 2017

Status

approved