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 A356200 Number of edge covers in the n-gear graph. 0
 3, 25, 162, 969, 5613, 32062, 181989, 1030017, 5821902, 32886505, 185714829, 1048619646, 5920559661, 33426829321, 188721717102, 1065481514817, 6015458406741, 33961820796094, 191740095366885, 1082517159435249, 6111623364952302, 34504707439240921 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence extended to a(1) using the formula/recurrence. LINKS Table of n, a(n) for n=1..22. Eric Weisstein's World of Mathematics, Edge Cover Eric Weisstein's World of Mathematics, Gear Graph Index entries for linear recurrences with constant coefficients, signature (9,-21,12,-2). FORMULA a(n) = (3-sqrt(7))^n + (sqrt(7)+3)^n - Lucas(2*n). a(n) = 9*a(n-1) - 21*a(n-2) + 12*a(n-3) - 2*a(n-4). G.f.: x*(3-2*x)/((1-3*x+x^2)*(1-6*x+2*x^2)). a(n) = 2*A146963(n) - A005248(n). - R. J. Mathar, Jan 25 2023 MATHEMATICA Table[(3 - Sqrt[7])^n + (3 + Sqrt[7])^n - LucasL[2 n], {n, 30}] // Expand CoefficientList[Series[(3 - 2 x)/((1 - 3 x + x^2) (1 - 6 x + 2 x^2)), {x, 0, 20}], x] LinearRecurrence[{9, -21, 12, -2}, {3, 25, 162, 969}, 20] CROSSREFS Sequence in context: A367507 A303602 A000544 * A221777 A227995 A037776 Adjacent sequences: A356197 A356198 A356199 * A356201 A356202 A356203 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jul 29 2022 STATUS approved

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Last modified August 13 02:23 EDT 2024. Contains 375113 sequences. (Running on oeis4.)