A083943 -id:A083943 - cp's OEIS frontend

A083944 A generalized Jacobsthal sequence.

0, 1, -2, -3, -10, -19, -42, -83, -170, -339, -682, -1363, -2730, -5459, -10922, -21843, -43690, -87379, -174762, -349523, -699050, -1398099, -2796202, -5592403, -11184810, -22369619, -44739242, -89478483, -178956970, -357913939, -715827882, -1431655763

Offset: 0

Paul Barry, May 09 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Cf. A083943.

[3/2-2^(n+1)/3-5*(-1)^n/6: n in [0..40]]; // Vincenzo Librandi, Apr 04 2012

CoefficientList[Series[x (1-4x)/((1+x)(1-x)(1-2x)),{x,0,40}],x] (* Vincenzo Librandi, Apr 04 2012 *)
LinearRecurrence[{2,1,-2},{0,1,-2},40] (* Harvey P. Dale, Jun 08 2014 *)

x='x+O('x^50); concat([0], Vec(x*(1-4*x)/((1+x)*(1-x)*(1-2*x)))) \\ G. C. Greubel, Oct 10 2017

G.f.: x*(1-4*x)/((1+x)*(1-x)*(1-2*x)).
E.g.f.: (9*exp(x) - 4*exp(2*x) - 5*exp(-x))/6.
a(n) = (9 - 2^(n+2) - 5*(-1)^n)/6.
a(n) = a(n-1) + 2*a(n-2) - 3 with n > 1, a(0)=0, a(1)=1.
a(2*n) = -A000975(2*n); a(2*n+1) = 2 - A000975(2*n+1).
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), with a(0)=0, a(1)=1, a(2)=-2. - Harvey P. Dale, Jun 08 2014

A159290 A generalized Jacobsthal sequence.

Original entry on oeis.org

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

Creighton Dement, Apr 08 2009

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')

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).

A083943, A068156

[-1 + (2*(-1)^n + 5*2^(n+1))/3: n in [0..50]]; // G. C. Greubel, Jun 27 2018

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 *)

x='x+O('x^50); Vec((3-x)/(-x^2+1-2*x+2*x^3)) \\ G. C. Greubel, Jun 27 2018

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

cp's OEIS Frontend

A083944 A generalized Jacobsthal sequence.

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