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 A022112 Fibonacci sequence beginning 2, 6. 12
 2, 6, 8, 14, 22, 36, 58, 94, 152, 246, 398, 644, 1042, 1686, 2728, 4414, 7142, 11556, 18698, 30254, 48952, 79206, 128158, 207364, 335522, 542886, 878408, 1421294, 2299702, 3720996, 6020698, 9741694, 15762392, 25504086, 41266478, 66770564, 108037042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For n>=3 the number of perfect matchings in the n-antiprism graph. - Andrew Howroyd, May 17 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Yun-Tak Oh, Hosho Katsura, Hyun-Yong Lee, Jung Hoon Han, Proposal of a spin-one chain model with competing dimer and trimer interactions, arXiv:1709.01344 [cond-mat.str-el], 2017. Eric Weisstein's World of Mathematics, Antiprism Graph Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Perfect Matching Eric Weisstein's World of Mathematics, Maximum Independent Edge Set Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA a(n) = 4*Fibonacci(n+2) - 2*Fibonacci(n+1). - Gary Detlefs Dec 21 2010 a(n) = 2*A000204(n+1). - R. J. Mathar, Mar 11 2011 G.f. ( -2-4*x ) / ( -1+x+x^2 ). - R. J. Mathar, Mar 11 2011 a(n) = Fibonacci(n-2) + Fibonacci(n+4). - Gary Detlefs, Mar 31 2012 a(n) = L(n - 1) + L(n) + L(n + 1), for n > 0, where L(n) is the n-th Lucas number (A000204). - Alonso del Arte, Sep 25 2013 a(n) = L(n + 3) - L(n). - Bruno Berselli, Jun 15 2017 From Colin Barker, Oct 27 2017: (Start) a(n) = (2^(-n)*((1-sqrt(5))^n*(-5+sqrt(5)) + (1+sqrt(5))^n*(5+sqrt(5)))) / sqrt(5). a(n) = a(n-1) + a(n-2) for > 1. (End) MATHEMATICA LinearRecurrence[{1, 1}, {2, 6}, 40] (* Harvey P. Dale, Apr 21 2012 *) 2 LucasL[Range[30]] (* Alonso del Arte, Sep 25 2013 *) PROG (Haskell) a022112 n = a022112_list !! n a022112_list = 2 : 6 : zipWith (+) (tail a022112_list) a022112_list -- Reinhard Zumkeller, Apr 08 2012 (PARI) a(n)=4*fibonacci(n+2)-2*fibonacci(n+1) \\ Charles R Greathouse IV, Oct 07 2015 (PARI) Vec(2*(1 + 2*x) / (1 - x - x^2) + O(x^60)) \\ Colin Barker, Oct 27 2017 CROSSREFS Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154. Sequence in context: A117588 A174229 A187217 * A107019 A269831 A048133 Adjacent sequences:  A022109 A022110 A022111 * A022113 A022114 A022115 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 19 02:36 EST 2018. Contains 318245 sequences. (Running on oeis4.)