This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082311 #35 Jul 15 2024 17:56:05
%S A082311 1,5,43,341,2731,21845,174763,1398101,11184811,89478485,715827883,
%T A082311 5726623061,45812984491,366503875925,2932031007403,23456248059221,
%U A082311 187649984473771,1501199875790165,12009599006321323,96076792050570581,768614336404564651,6148914691236517205
%N A082311 A Jacobsthal sequence trisection.
%H A082311 Vincenzo Librandi, <a href="/A082311/b082311.txt">Table of n, a(n) for n = 0..1000</a>
%H A082311 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,8).
%F A082311 a(n) = (2*8^n + (-1)^n)/3 = A001045(3*n+1).
%F A082311 From _R. J. Mathar_, Feb 23 2009: (Start)
%F A082311 a(n) = 7*a(n-1) + 8*a(n-2).
%F A082311 G.f.: (1-2*x)/((1+x)*(1-8*x)). (End)
%F A082311 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 A082311 a(n)= A007613(n) + A132805(n) = A081374(1+3*n). - _Paul Curtz_, Jun 06 2011
%F A082311 E.g.f.: (cosh(x) + 2*cosh(8*x) - sinh(x) + 2*sinh(8*x))/3. - _Stefano Spezia_, Jul 15 2024
%t A082311 f[n_] := (2*8^n + (-1)^n)/3; Array[f, 25, 0] (* _Robert G. Wilson v_, Aug 13 2011 *)
%o A082311 (Magma)[2*8^n/3+(-1)^n/3 : n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011
%o A082311 (PARI) x='x+O('x^30); Vec((1-2*x)/((1+x)*(1-8*x))) \\ _G. C. Greubel_, Sep 16 2018
%Y A082311 Cf. A001045, A007613, A015565, A024494, A070366, A081374, A082365, A132805.
%K A082311 easy,nonn
%O A082311 0,2
%A A082311 _Paul Barry_, Apr 09 2003