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 A097164 #18 Jul 11 2023 19:35:02
%S A097164 1,4,8,20,36,84,148,340,596,1364,2388,5460,9556,21844,38228,87380,
%T A097164 152916,349524,611668,1398100,2446676,5592404,9786708,22369620,
%U A097164 39146836,89478484,156587348,357913940,626349396,1431655764,2505397588
%N A097164 Expansion of (1+3x)/((1-x)(1-4x^2)).
%C A097164 Partial sums of A084221. a(n) = A097163(n+1)/4. Third binomial transform is A097165.
%C A097164 a(n+1) = 4*A097163(n). - _Zerinvary Lajos_, Mar 17 2008
%C A097164 See A133628 for an essentially identical sequence. - _R. J. Mathar_, Jun 08 2008
%H A097164 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4).
%F A097164 a(n) = 5*2^n/2 - (-2)^n/6 - 4/3;
%F A097164 a(n) = a(n-1) + 4a(n-2) - 4a(n-3).
%F A097164 G.f. ( 1+3*x ) / ( (x-1)*(2*x+1)*(2*x-1) ). - _R. J. Mathar_, Jul 06 2011
%p A097164 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=4*a[n-2]+4 od: seq(a[n], n=1..31); # _Zerinvary Lajos_, Mar 17 2008
%t A097164 CoefficientList[Series[(1+3x)/((1-x)(1-4x^2)),{x,0,50}],x] (* or *) LinearRecurrence[{1,4,-4},{1,4,8},50] (* _Harvey P. Dale_, Jul 11 2023 *)
%K A097164 easy,nonn
%O A097164 0,2
%A A097164 _Paul Barry_, Jul 30 2004