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
Links
- 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).
Programs
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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]
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).