A082311 - OEIS

%I #35 Jul 15 2024 17:56:05

%S 1,5,43,341,2731,21845,174763,1398101,11184811,89478485,715827883,

%T 5726623061,45812984491,366503875925,2932031007403,23456248059221,

%U 187649984473771,1501199875790165,12009599006321323,96076792050570581,768614336404564651,6148914691236517205

%N A Jacobsthal sequence trisection.

%H Vincenzo Librandi, <a href="/A082311/b082311.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,8).

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

%F From _R. J. Mathar_, Feb 23 2009: (Start)

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

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

%F a(n) = A024494(3*n+1). a(n) = 8*a(n-1) + 3*(-1)^n. Sum of digits = A070366. - _Paul Curtz_, Nov 20 2007

%F a(n)= A007613(n) + A132805(n) = A081374(1+3*n). - _Paul Curtz_, Jun 06 2011

%F E.g.f.: (cosh(x) + 2*cosh(8*x) - sinh(x) + 2*sinh(8*x))/3. - _Stefano Spezia_, Jul 15 2024

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

%o (Magma)[2*8^n/3+(-1)^n/3 : n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011

%o (PARI) x='x+O('x^30); Vec((1-2*x)/((1+x)*(1-8*x))) \\ _G. C. Greubel_, Sep 16 2018

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

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 09 2003