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 A117591 2^n + Fibonacci(n). 8
 1, 3, 5, 10, 19, 37, 72, 141, 277, 546, 1079, 2137, 4240, 8425, 16761, 33378, 66523, 132669, 264728, 528469, 1055341, 2108098, 4212015, 8417265, 16823584, 33629457, 67230257, 134414146, 268753267, 537385141, 1074573864, 2148829917 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(3n) is even if n>0. - Robert G. Wilson v, Sep 06 2002 3 divides a(8n+1) and a(8n-1). - Enrique Pérez Herrero, Dec 29 2010 a(n) = A000079(n+1) - A099036(n) = A099036(n) + 2 * A000045(n). - Reinhard Zumkeller, Aug 15 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-2). FORMULA G.f. (1-3x^2)/((1-x-x^2)*(1-2x)). MATHEMATICA Table[f=Fibonacci[n]; 2^n+f, {n, 1, 40, 1}] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *) CoefficientList[Series[(1 - 3 x^2)/((1 - x - x^2) (1 - 2 x)), {x, 0, 35}], x] (* Vincenzo Librandi, Nov 02 2014 *) PROG (Haskell) a117591 n = a117591_list !! n a117591_list = zipWith (+) a000079_list a000045_list -- Reinhard Zumkeller, Aug 15 2013 (MAGMA) [2^n+Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Nov 02 2014 (PARI) a(n)=2^n + fibonacci(n) \\ Charles R Greathouse IV, Oct 07 2016 CROSSREFS Cf. A000045, A000079, A074824, A001611, A212262. Sequence in context: A133999 A238431 A014610 * A003055 A317766 A217925 Adjacent sequences:  A117588 A117589 A117590 * A117592 A117593 A117594 KEYWORD nonn,easy AUTHOR Franklin T. Adams-Watters, Apr 04 2006 STATUS approved

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Last modified May 28 13:20 EDT 2020. Contains 334683 sequences. (Running on oeis4.)