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 A083336 #13 Dec 14 2024 12:45:27
%S A083336 3,3,9,12,33,45,123,168,459,627,1713,2340,6393,8733,23859,32592,89043,
%T A083336 121635,332313,453948,1240209,1694157,4628523,6322680,17273883,
%U A083336 23596563,64467009,88063572,240594153,328657725,897909603,1226567328,3351044259,4577611587,12506267433
%N A083336 a(n) = 4*a(n-2) - a(n-4).
%C A083336 a(n)/A002531(n+1) converges to sqrt(3).
%H A083336 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-1).
%F A083336 a(2*n) = A082841(n) = a(2*n-1) + 3*A002531(2*n).
%F A083336 a(2*n+1) = (a(2*n) + 3*A002531(2*n+1)) / 2.
%F A083336 G.f.: (3 + 3*x - 3*x^2) / (1 - 4*x^2 + x^4).
%t A083336 CoefficientList[Series[(3+3x-3x^2)/(1-4x^2+x^4), {x, 0, 30}], x]
%t A083336 Transpose[NestList[Flatten[{Rest[#],4#[[3]]-First[#]}]&, {3,3,9,12}, 50]][[1]] (* _Harvey P. Dale_, Mar 26 2011 *)
%t A083336 LinearRecurrence[{0, 4, 0, -1}, {3, 3, 9, 12}, 30] (* _T. D. Noe_, Mar 26 2011 *)
%K A083336 nonn,easy
%O A083336 0,1
%A A083336 Mario Catalani (mario.catalani(AT)unito.it), Apr 26 2003