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 A025169 a(n) = 2*F(2*n+2), where F(n)=A000045(n) (the Fibonacci sequence). 13
 2, 6, 16, 42, 110, 288, 754, 1974, 5168, 13530, 35422, 92736, 242786, 635622, 1664080, 4356618, 11405774, 29860704, 78176338, 204668310, 535828592, 1402817466, 3672623806, 9615053952, 25172538050, 65902560198, 172535142544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The pairs (x, y) = (a(n), a(n+1)) satisfy  x^2 + y^2 = 3*x*y + 4. - Michel Lagneau, Feb 01 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials, arXiv:1502.03085 [math.NT], 2015 (see p. 32). Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (3,-1). FORMULA G.f.: 2/(1 - 3*x + x^2). a(n) = 3*a(n-1) - a(n-2). a(n) = 2*A001906(n+1). a(n) = A111282(n+2). - Reinhard Zumkeller, Apr 08 2012 a(n) = Fibonacci(2*n+1) + Lucas(2*n+1). - Bruno Berselli, Oct 13 2017 MATHEMATICA Table[2 Fibonacci[2 n + 2], {n, 0, 26}] (* or *) CoefficientList[Series[2/(1 - 3 x + x^2), {x, 0, 26}], x] (* Michael De Vlieger, Mar 09 2016 *) LinearRecurrence[{3, -1}, {2, 6}, 27] (* Jean-François Alcover, Sep 27 2017 *) PROG (PARI) a(n)=2*fibonacci(2*n+2) (MAGMA) [2*Fibonacci(2*n+2): n in [0..30]]; // Vincenzo Librandi, Jul 11 2011 (Haskell) a025169 n = a025169_list !! n a025169_list = 2 : 6 : zipWith (-) (map (* 3) \$ tail a025169_list) a025169_list -- Reinhard Zumkeller, Apr 08 2012 CROSSREFS Cf. A000032, A000045, A001906, A002878, A122367. Sequence in context: A217194 A156664 * A111282 A115730 A191694 A224232 Adjacent sequences:  A025166 A025167 A025168 * A025170 A025171 A025172 KEYWORD nonn,easy AUTHOR EXTENSIONS Better description from Michael Somos STATUS approved

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