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 A159290 A generalized Jacobsthal sequence. 1
 3, 5, 13, 25, 53, 105, 213, 425, 853, 1705, 3413, 6825, 13653, 27305, 54613, 109225, 218453, 436905, 873813, 1747625, 3495253, 6990505, 13981013, 27962025, 55924053, 111848105, 223696213, 447392425, 894784853, 1789569705, 3579139413 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sequence generated by the floretion: X*Y with X = 0.5('i + 'j + 'k + 'ee') and Y = 0.5(i' + j' + k' + 'ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj' + 'ee') LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Creighton Dement, Online Floretion Multiplier [broken link] Index entries for linear recurrences with constant coefficients, signature (2,1,-2). FORMULA a(n) = -1 + (2*(-1)^n + 5*2^(n+1))/3. G.f.: (3-x)/((1-x)*(1+x)*(1-2*x)). a(n) = 3*A000975(n+1) - A000975(n). - R. J. Mathar, Sep 11 2019 a(n)+a(n+1) = A051633(n+1). - R. J. Mathar, Mar 23 2023 MATHEMATICA LinearRecurrence[{2, 1, -2}, {3, 5, 13}, 50] (* or *) Table[-1 + (2*(-1)^n + 5*2^(n+1))/3, {n, 0, 30}] (* G. C. Greubel, Jun 27 2018 *) PROG (PARI) x='x+O('x^50); Vec((3-x)/(-x^2+1-2*x+2*x^3)) \\ G. C. Greubel, Jun 27 2018 (Magma) [-1 + (2*(-1)^n + 5*2^(n+1))/3: n in [0..50]]; // G. C. Greubel, Jun 27 2018 CROSSREFS A083943, A068156 Sequence in context: A026709 A219699 A320330 * A110494 A098615 A026720 Adjacent sequences: A159287 A159288 A159289 * A159291 A159292 A159293 KEYWORD easy,nonn AUTHOR Creighton Dement, Apr 08 2009 STATUS approved

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Last modified May 23 00:00 EDT 2024. Contains 372758 sequences. (Running on oeis4.)