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 A102345 #79 Mar 13 2025 12:14:07
%S A102345 2,2,10,26,82,242,730,2186,6562,19682,59050,177146,531442,1594322,
%T A102345 4782970,14348906,43046722,129140162,387420490,1162261466,3486784402,
%U A102345 10460353202,31381059610,94143178826,282429536482,847288609442
%N A102345 a(n) = 3^n + (-1)^n.
%C A102345 a(n) = A105723(n) + 2*(-1)^n; (a(n) + A105723(n))/2 = A000244(n). - _Reinhard Zumkeller_, Apr 18 2005
%H A102345 Michael De Vlieger, <a href="/A102345/b102345.txt">Table of n, a(n) for n = 0..2095</a>
%H A102345 Weerayuth Nilsrakoo and Achariya Nilsrakoo, <a href="https://doi.org/10.37394/23206.2025.24.7">On One-Parameter Generalization of Jacobsthal Numbers</a>, WSEAS Trans. Math. (2025) Vol. 24, 51-61. See p. 3.
%H A102345 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F A102345 a(n) = 2*a(n-1) + 3*a(n-2).
%F A102345 From _Elmo R. Oliveira_, Dec 18 2023: (Start)
%F A102345 G.f.: 2*(1-x)/((1+x)*(1-3*x)).
%F A102345 E.g.f.: exp(-x) + exp(3*x).
%F A102345 a(n) = 2*A046717(n). (End)
%t A102345 Table[3^n+(-1)^n,{n,0,30}] (* or *) LinearRecurrence[{2,3},{2,2},30] (* _Harvey P. Dale_, Jun 19 2016 *)
%o A102345 (Sage) [lucas_number2(n,2,-3) for n in range(0, 26)] # _Zerinvary Lajos_, Apr 30 2009
%Y A102345 Apart from leading term, same as A084182.
%Y A102345 Cf. A000244, A046717, A105723.
%K A102345 easy,nonn
%O A102345 0,1
%A A102345 _Graeme McRae_, Feb 16 2005