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%I #75 Feb 03 2024 18:13:57
%S 2,2,10,26,82,242,730,2186,6562,19682,59050,177146,531442,1594322,
%T 4782970,14348906,43046722,129140162,387420490,1162261466,3486784402,
%U 10460353202,31381059610,94143178826,282429536482,847288609442
%N a(n) = 3^n + (-1)^n.
%C a(n) = A105723(n) + 2*(-1)^n; (a(n) + A105723(n))/2 = A000244(n). - _Reinhard Zumkeller_, Apr 18 2005
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F a(n) = 2*a(n-1) + 3*a(n-2).
%F From _Elmo R. Oliveira_, Dec 18 2023: (Start)
%F G.f.: 2*(1-x)/((1+x)*(1-3*x)).
%F E.g.f.: exp(-x) + exp(3*x).
%F a(n) = 2*A046717(n). (End)
%t Table[3^n+(-1)^n,{n,0,30}] (* or *) LinearRecurrence[{2,3},{2,2},30] (* _Harvey P. Dale_, Jun 19 2016 *)
%o (Sage) [lucas_number2(n,2,-3) for n in range(0, 26)] # _Zerinvary Lajos_, Apr 30 2009
%Y Apart from leading term, same as A084182.
%Y Cf. A000244, A046717, A105723.
%K easy,nonn
%O 0,1
%A _Graeme McRae_, Feb 16 2005
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