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

Author

Paul Barry, Apr 09 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,8).

Crossrefs

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

Programs

Magma

[2*8^n/3+(-1)^n/3 : n in [0..30]]; // Vincenzo Librandi, Aug 13 2011

Mathematica

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

PARI

x='x+O('x^30); Vec((1-2*x)/((1+x)*(1-8*x))) \\ G. C. Greubel, Sep 16 2018

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