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 A130707 #22 Dec 16 2023 17:00:35
%S A130707 1,2,2,2,4,10,22,44,86,170,340,682,1366,2732,5462,10922,21844,43690,
%T A130707 87382,174764,349526,699050,1398100,2796202,5592406,11184812,22369622,
%U A130707 44739242,89478484,178956970,357913942,715827884,1431655766,2863311530
%N A130707 a(n+3) = 3*(a(n+2) - a(n+1)) + 2*a(n).
%C A130707 Binomial transform of period-3 sequence with period 1 1 -1.
%H A130707 Harvey P. Dale, <a href="/A130707/b130707.txt">Table of n, a(n) for n = 0..1000</a>
%H A130707 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2).
%F A130707 a(n) = 2^n/3 + 4*(-1)^n*(1/3)*cos((2n+1)*Pi/3). - _Emeric Deutsch_, Jul 27 2007
%F A130707 From _R. J. Mathar_, Nov 18 2007: (Start)
%F A130707 G.f.: (-1+x+x^2)/(2*x-1)/(x^2-x+1).
%F A130707 a(n) = (2*A057079(n) + 2^n)/3. (End)
%p A130707 a:=proc(n) options operator, arrow: (1/3)*2^n+(4/3)*(-1)^n*cos((1/3)*(2*n+1)*Pi) end proc: seq(a(n), n = 0 .. 33); # _Emeric Deutsch_, Jul 27 2007
%t A130707 RecurrenceTable[{a[0]==1,a[1]==a[2]==2,a[n]==3(a[n-1]-a[n-2])+2a[n-3]},a,{n,40}] (* or *) LinearRecurrence[{3,-3,2},{1,2,2},40] (* _Harvey P. Dale_, Jan 18 2015 *)
%K A130707 nonn
%O A130707 0,2
%A A130707 _Paul Curtz_, Jul 01 2007
%E A130707 More terms from _Emeric Deutsch_, Jul 27 2007