A356198 Number of edge covers in the n-book graph.

5, 41, 233, 1217, 6185, 31121, 155993, 780737, 3905225, 19529201, 97652153, 488273057, 2441389865, 12206998481, 61035090713, 305175650177, 1525878644105, 7629394006961, 38146971607673, 190734861184097, 953674312211945, 4768371573642641

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Book Graph

Eric Weisstein's World of Mathematics, Edge Cover

Index entries for linear recurrences with constant coefficients, signature (8,-17,10).

Formula

a(n) = 2*5^n - 2^(n + 1) - 1.

G.f.: x*(10*x^2-x-5)/((x-1)*(2*x-1)*(5*x-1)).

a(n) = 8*a(n-1) - 17*a(n-2) + 10*a(n-3).

a(n) = 2*A005057(n) - 1 = 6*A016127(n-1) - 1. - Hugo Pfoertner, Jul 29 2022

Mathematica

Table[2 5^n - 2^(n + 1) - 1, {n, 20}]
LinearRecurrence[{8, -17, 10}, {5, 41, 233}, 20]
CoefficientList[Series[(10 x^2 - x - 5)/((x - 1) (2 x - 1) (5 x - 1)), {x, 0, 20}], x]

Crossrefs

Cf. A005057, A016127.

Sequence in context: A270211 A270182 A273313 * A198725 A190638 A083300

Adjacent sequences: A356195 A356196 A356197 * A356199 A356200 A356201

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Jul 29 2022

Status

approved