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 A014113 a(n) = a(n-1) + 2*a(n-2) with a(0)=0, a(1)=2. 9
 0, 2, 2, 6, 10, 22, 42, 86, 170, 342, 682, 1366, 2730, 5462, 10922, 21846, 43690, 87382, 174762, 349526, 699050, 1398102, 2796202, 5592406, 11184810, 22369622, 44739242, 89478486, 178956970, 357913942, 715827882, 1431655766, 2863311530, 5726623062, 11453246122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 457 Index entries for linear recurrences with constant coefficients, signature (1,2). FORMULA a(0) = 0 and if n>=1, a(n) = 2^n - a(n-1). a(n) = A078008(n+1). - Reinhard Zumkeller, Jun 10 2005 a(n) = 2*A001045(n). - Benoit Jubin, Dec 01 2011 a(n) = (2^(n+1) - 2*(-1)^n)/3. - Ralf Stephan, Jul 18 2013 G.f.: 2*x/(1+x)/(1-2*x). - Colin Barker, Feb 19 2012 G.f.: 1/Q(0) -1, where Q(k) = 1 + 2*x^2 - (2*k+3)*x + x*(2*k+1 - 2*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013 MATHEMATICA LinearRecurrence[{1, 2}, {0, 2}, 50] (* Vincenzo Librandi, Feb 19 2012 *) PROG (Haskell) a014113 n = a014113_list !! n a014113_list = 0 : 2 : zipWith (+) (map (* 2) a014113_list) (tail a014113_list) -- Reinhard Zumkeller, Jul 20 2013 CROSSREFS Cf. A001045, A078008, A163271, A290732. Sequence in context: A019310 A078008 A151575 * A284462 A262278 A265639 Adjacent sequences: A014110 A014111 A014112 * A014114 A014115 A014116 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)