A356198 - OEIS

%I #13 Feb 16 2025 08:34:03

%S 5,41,233,1217,6185,31121,155993,780737,3905225,19529201,97652153,

%T 488273057,2441389865,12206998481,61035090713,305175650177,

%U 1525878644105,7629394006961,38146971607673,190734861184097,953674312211945,4768371573642641

%N Number of edge covers in the n-book graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BookGraph.html">Book Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-17,10).

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

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

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

%F a(n) = 2*A005057(n) - 1 = 6*A016127(n-1) - 1. - _Hugo Pfoertner_, Jul 29 2022

%t Table[2 5^n - 2^(n + 1) - 1, {n, 20}]

%t LinearRecurrence[{8, -17, 10}, {5, 41, 233}, 20]

%t CoefficientList[Series[(10 x^2 - x - 5)/((x - 1) (2 x - 1) (5 x - 1)), {x, 0, 20}], x]

%Y Cf. A005057, A016127.

%K nonn,easy,changed

%O 1,1

%A _Eric W. Weisstein_, Jul 29 2022