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 A097163 #23 Jun 13 2015 00:51:29
%S A097163 1,2,5,9,21,37,85,149,341,597,1365,2389,5461,9557,21845,38229,87381,
%T A097163 152917,349525,611669,1398101,2446677,5592405,9786709,22369621,
%U A097163 39146837,89478485,156587349,357913941,626349397,1431655765,2505397589
%N A097163 Expansion of (1+x-x^2)/((1-x)*(1-4*x^2)).
%C A097163 Interleave (4*4^n-1)/2 (see A002450) and (7*4^n-1)/3 (A206374).
%H A097163 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4).
%F A097163 G.f.: (1+x-x^2)/((1-x)*(1-4*x^2)).
%F A097163 a(n) = 5*2^n/4+(-2)^n/12-1/3.
%F A097163 a(n) = a(n-1)+4*a(n-2)-4*a(n-3).
%F A097163 a(2*n) = A002450(n+1).
%F A097163 a(n) = A097164(n+1)/4.
%F A097163 a(n) = (15*2^n-(-2)^n-8)/24. - _Harvey P. Dale_, Jun 17 2011
%p A097163 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=4*a[n-2]+4 od: seq(a[n]/4, n=2..33); # _Zerinvary Lajos_, Mar 17 2008
%t A097163 CoefficientList[Series[(1+x-x^2)/((1-x)(1-4x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{1,4,-4},{1,2,5},41] (* or *) f[n_]:=(15*2^n-(-2)^n - 8)/24; Array[f, 40] (* _Harvey P. Dale_, Jun 17 2011 *)
%K A097163 nonn,easy
%O A097163 0,2
%A A097163 _Paul Barry_, Jul 30 2004