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 A061705 Number of matchings in the wheel graph with n spokes. 3
 2, 5, 10, 19, 36, 66, 120, 215, 382, 673, 1178, 2050, 3550, 6121, 10514, 17999, 30720, 52290, 88788, 150427, 254342, 429245, 723190, 1216514, 2043386, 3427661, 5742490, 9609355, 16062492, 26821698, 44744688, 74576735, 124192270, 206650201, 343594514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also the number of maximal matchings in the n-helm graph. - Eric W. Weisstein, May 27 2017 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Helm Graph Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximal Independent Edge Set Eric Weisstein's World of Mathematics, Wheel Graph Index entries for linear recurrences with constant coefficients, signature (2, 1, -2, -1). FORMULA G.f.: x*(2 + x - 2*x^2 - 2*x^3) / (1 - x - x^2)^2. a(n) = (n+1)*Fibonacci(n) + 2*Fibonacci(n-1). a(n) = sqrt(5)*((n+1)*(u^n - v^n) + 2*(u^(n-1) - v^(n-1)))/5, where u = (1+sqrt(5))/2, v = (1-sqrt(5))/2. a(0)=2, a(1)=5, a(2)=10, a(3)=19; for n > 3, a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4). - Harvey P. Dale, Jun 05 2011 a(n) = n*Fibonacci(n) + Lucas(n) = (n+1)*Fibonacci(n+1) - (n-1)*Fibonacci(n-1). - Bruno Berselli, May 26 2015 EXAMPLE a(3)=10 because the matchings in a wheel graph with spokes OA, OB and OC are the empty set, {AB}, {BC}, {CA}, {OA}, {OB}, {OC}, {OA, BC}, {OB, CA}, {OC, AB}. MATHEMATICA Rest[CoefficientList[Series[x (2 + x - 2 x^2 - 2 x^3)/(1 - x - x^2)^2, {x, 0, 40}], x]] (* Harvey P. Dale, Jun 05 2011 *) LinearRecurrence[{2, 1, -2, -1}, {2, 5, 10, 19}, 40] (* Harvey P. Dale, Jun 05 2011 *) Table[n Fibonacci[n] + LucasL[n], {n, 40}] (* Eric W. Weisstein, Mar 31 2017 *) PROG (MAGMA) [n*Fibonacci(n) + Lucas(n): n in [1..50]]; // Vincenzo Librandi, Jan 14 2016 (PARI) Vec(x*(2+x-2*x^2-2*x^3)/(1-x-x^2)^2 + O(x^50)) \\ Colin Barker, Mar 09 2016 CROSSREFS Cf. A000032, A000045. Cf. A258321: Fibonacci(n) + n*Lucas(n). Sequence in context: A288579 A065613 A249557 * A052944 A132736 A263366 Adjacent sequences:  A061702 A061703 A061704 * A061706 A061707 A061708 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 18 2001 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)