A082311 A Jacobsthal sequence trisection.

1, 5, 43, 341, 2731, 21845, 174763, 1398101, 11184811, 89478485, 715827883, 5726623061, 45812984491, 366503875925, 2932031007403, 23456248059221, 187649984473771, 1501199875790165, 12009599006321323, 96076792050570581, 768614336404564651, 6148914691236517205

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,8).

Formula

a(n) = (2*8^n + (-1)^n)/3 = A001045(3*n+1).

From R. J. Mathar, Feb 23 2009: (Start)

a(n) = 7*a(n-1) + 8*a(n-2).

G.f.: (1-2*x)/((1+x)*(1-8*x)). (End)

a(n) = A024494(3*n+1). a(n) = 8*a(n-1) + 3*(-1)^n. Sum of digits = A070366. - Paul Curtz, Nov 20 2007

a(n)= A007613(n) + A132805(n) = A081374(1+3*n). - Paul Curtz, Jun 06 2011

E.g.f.: (cosh(x) + 2*cosh(8*x) - sinh(x) + 2*sinh(8*x))/3. - Stefano Spezia, Jul 15 2024

Mathematica

f[n_] := (2*8^n + (-1)^n)/3; Array[f, 25, 0] (* Robert G. Wilson v, Aug 13 2011 *)

Prog

(Magma)[2*8^n/3+(-1)^n/3 : n in [0..30]]; // Vincenzo Librandi, Aug 13 2011
(PARI) x='x+O('x^30); Vec((1-2*x)/((1+x)*(1-8*x))) \\ G. C. Greubel, Sep 16 2018

Crossrefs

Cf. A001045, A007613, A015565, A024494, A070366, A081374, A082365, A132805.

Sequence in context: A182191 A038140 A178826 * A269121 A326884 A241707

Adjacent sequences: A082308 A082309 A082310 * A082312 A082313 A082314

Keyword

easy,nonn

Author

Paul Barry, Apr 09 2003

Status

approved