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 A117863 #18 Apr 06 2024 05:43:55
%S A117863 3,6,18,30,78,126,318,510,1278,2046,5118,8190,20478,32766,81918,
%T A117863 131070,327678,524286,1310718,2097150,5242878,8388606,20971518,
%U A117863 33554430,83886078,134217726,335544318,536870910,1342177278,2147483646,5368709118,8589934590
%N A117863 Number of palindromes (in base 4) below 4^n.
%H A117863 Harvey P. Dale, <a href="/A117863/b117863.txt">Table of n, a(n) for n = 1..1000</a>
%H A117863 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4).
%F A117863 a(n) = 5*4^((n-1)/2)-2 (n odd), 2*4^(n/2)-2 (n even).
%F A117863 G.f.: 3*x*(x+1) / ((x-1)*(2*x-1)*(2*x+1)). [_Colin Barker_, Feb 15 2013]
%F A117863 a(1)=3, a(2)=6, a(3)=18, a(n)=a(n-1)+4*a(n-2)-4*a(n-3). - _Harvey P. Dale_, May 09 2013
%t A117863 Rest[CoefficientList[Series[3x (x+1)/((x-1)(2x-1)(2x+1)),{x,0,40}],x]] (* or *) LinearRecurrence[{1,4,-4},{3,6,18},40] (* _Harvey P. Dale_, May 09 2013 *)
%Y A117863 Cf. A050250.
%K A117863 nonn,base,easy
%O A117863 1,1
%A A117863 _Martin Renner_, May 02 2006
%E A117863 More terms from _Colin Barker_, Feb 15 2013