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 A168642 a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1. 3
 1, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, 715827883, 1431655765, 2863311531 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = A001045(n+3) for n > 0. First differences of A085278. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (1,2). FORMULA a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 5, a(2) = 11. G.f.: (1 + 2*x)^2/((1+x)*(1-2*x)). E.g.f.: (1/3)*(8*exp(2*x) + exp(-x)). - G. C. Greubel, Jul 28 2016 MATHEMATICA Table[(8*2^n + (-1)^n)/3, {n, 0, 50}] (* or *) LinearRecurrence[{1, 2}, {1, 5}, 25] (* G. C. Greubel, Jul 28 2016 *) PROG (MAGMA) [1] cat [ (8*2^n+(-1)^n)/3: n in [1..30] ]; (PARI) a(n)=([0, 1; 2, 1]^n*[1; 5])[1, 1] \\ Charles R Greathouse IV, Jul 29 2016 CROSSREFS Cf. A001045 (Jacobsthal sequence), A085278 (expansion of (1+2x)^2/((1-x^2)(1-2x)). Sequence in context: A166863 A163704 A131898 * A234597 A261982 A296033 Adjacent sequences:  A168639 A168640 A168641 * A168643 A168644 A168645 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Dec 01 2009 STATUS approved

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Last modified September 20 06:17 EDT 2019. Contains 327212 sequences. (Running on oeis4.)