A159290 A generalized Jacobsthal sequence.

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

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