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 A083314 #8 Sep 29 2016 11:26:39
%S A083314 1,3,12,51,216,903,3732,15291,62256,252303,1019052,4105731,16511496,
%T A083314 66311703,266043972,1066567371,4273443936,17115299103,68525766492,
%U A083314 274296776211,1097768235576,4392816334503,17576495514612,70321672588251
%N A083314 (2*4^n-(3^n-1))/2.
%C A083314 Binomial transform of A083313
%H A083314 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12)
%F A083314 a(n)=(2*4^n-(3^n-1))/2
%F A083314 G.f. (1-5x+7x^2)/((1-x)(1-3x)(1-4x))
%F A083314 E.g.f. (2exp(4x)-exp(3x)+exp(x))/2
%t A083314 Table[(2*4^n-(3^n-1))/2,{n,0,30}] (* or *) LinearRecurrence[{8,-19,12},{1,3,12},30] (* _Harvey P. Dale_, Sep 29 2016 *)
%Y A083314 Cf. A083315.
%K A083314 easy,nonn
%O A083314 0,2
%A A083314 _Paul Barry_, Apr 24 2003