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 A118658 a(n) = 2*F(n-1) = L(n) - F(n), where F(n) and L(n) are Fibonacci and Lucas numbers respectively. 14
 2, 0, 2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Essentially the same as A006355, A047992, A054886, A055389, A068922, A078642, A090991. - Philippe Deléham, Sep 20 2006 and Georg Fischer, Oct 07 2018 Also the number of matchings in the (n-2)-pan graph. - Eric W. Weisstein, Jun 30 2016 Also the number of maximal independent vertex sets (and minimal vertex covers) in the (n-1)-ladder graph. - Eric W. Weisstein, Jun 30 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Ladder Graph Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set Eric Weisstein's World of Mathematics, Minimal Vertex Cover Eric Weisstein's World of Mathematics, Pan Graph Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA From Philippe Deléham, Sep 20 2006: (Start) a(0)=2, a(1)=0; for n > 1, a(n) = a(n-1) + a(n-2). G.f. (2 - 2*x)/(1 - x - x^2). a(0)=2 and a(n) = 2*A000045(n-1) for n > 0. (End) a(n) = A006355(n) + 0^n. - M. F. Hasler, Nov 05 2014 a(n) = Lucas(n-2) + Fibonacci(n-2). - Bruno Berselli, May 27 2015 a(n) = 3*Fibonacci(n-2) + Fibonacci(n-5). - Bruno Berselli, Feb 20 2017 a(n) = 2*A212804(n). - Bruno Berselli, Feb 21 2017 E.g.f.: 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) - sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Apr 18 2022 MAPLE with(combinat): seq(2*fibonacci(n-1), n=0..40); # Muniru A Asiru, Oct 07 2018 a := n -> -2*I^n*ChebyshevU(n-2, -I/2): seq(simplify(a(n)), n = 0..39); # Peter Luschny, Dec 03 2023 MATHEMATICA LinearRecurrence[{1, 1}, {2, 0}, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 05 2011 *) Table[LucasL[n] - Fibonacci[n], {n, 0, 40}] (* Vincenzo Librandi, Sep 14 2014 *) Table[2 Fibonacci[n - 1], {n, 0, 20}] (* Eric W. Weisstein, Jun 30 2017 *) 2 Fibonacci[Range[0, 20] - 1] (* Eric W. Weisstein, Jun 30 2017 *) Subtract @@@ (Through[{LucasL, Fibonacci}[#]] & /@ Range[0, 20]) (* Eric W. Weisstein, Jun 30 2017 *) CoefficientList[Series[(2 (-1 + x))/(-1 + x + x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 30 2017 *) PROG (PARI) a(n)=fibonacci(n-1)<<1 \\ Charles R Greathouse IV, Jun 05 2011 (Magma) [Lucas(n) - Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Sep 14 2014 (GAP) List([0..40], n->2*Fibonacci(n-1)); # Muniru A Asiru, Oct 07 2018 CROSSREFS Cf. A000032, A000045, A003714, A212804. Sequence in context: A273166 A331262 A300822 * A165912 A301823 A301999 Adjacent sequences: A118655 A118656 A118657 * A118659 A118660 A118661 KEYWORD nonn,easy AUTHOR Bill Jones (b92057(AT)yahoo.com), May 18 2006 EXTENSIONS More terms from Philippe Deléham, Sep 20 2006 Corrected by T. D. Noe, Nov 01 2006 STATUS approved

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Last modified August 10 05:32 EDT 2024. Contains 375044 sequences. (Running on oeis4.)