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 A174443 Generating function x/(1+4*x-8*x^2). 2
 0, 1, -4, 24, -128, 704, -3840, 20992, -114688, 626688, -3424256, 18710528, -102236160, 558628864, -3052404736, 16678649856, -91133837312, 497964548096, -2720928890880, 14867431948288, -81237158920192, 443888091267072, -2425449636429824, 13252903275855872 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binet form: with a = 4/(1 + sqrt(3)); b = 4/(1 - sqrt(3)); we have a(n)=(a^n - b^n)/(a - b). Alternative expressions for the roots are -2 +- 2*sqrt(3). Limiting ratio a(n+1)/a(n) is:-5.464101615137755== -2-2*sqrt(3). LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..500 FORMULA a(0)=0, a(1)=1, a(n) = -4a(n-1) + 8a(n-2). a(0)=0, a(n) = (-2)^(n-1)*A002605(n). MATHEMATICA a = 4/(1 + Sqrt[3]); b = 4/(1 - Sqrt[3]); f[n_] = (a^n - b^n)/(a - b); Table[FullSimplify[f[n]], {n, 0, 30}] CROSSREFS Cf. A180222 (unsigned version of this sequence). Sequence in context: A024049 A103455 A289715 * A180222 A192070 A048180 Adjacent sequences:  A174440 A174441 A174442 * A174444 A174445 A174446 KEYWORD sign,easy AUTHOR Roger L. Bagula, Nov 28 2010 EXTENSIONS Correction of the Mathematica code and better name by Joerg Arndt. Formulae and edited by Ralf Stephan, Nov 27 2010 STATUS approved

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)