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 A117867 #21 Oct 30 2016 13:17:16
%S A117867 7,14,70,126,574,1022,4606,8190,36862,65534,294910,524286,2359294,
%T A117867 4194302,18874366,33554430,150994942,268435454,1207959550,2147483646,
%U A117867 9663676414,17179869182,77309411326,137438953470,618475290622,1099511627774,4947802324990
%N A117867 Number of palindromes (in base 8) below 8^n.
%H A117867 G. C. Greubel, <a href="/A117867/b117867.txt">Table of n, a(n) for n = 1..1000</a>
%H A117867 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,8,-8).
%F A117867 a(n) = 9*8^((n-1)/2)-2 (n odd), 2*8^(n/2)-2 (n even).
%F A117867 G.f.: 7*x*(x+1) / ((x-1)*(8*x^2-1)). - _Colin Barker_, Feb 15 2013
%F A117867 From _G. C. Greubel_, Oct 27 2016: (Start)
%F A117867 a(n) = a(n-1) + 8*a(n-2) - 8*a(n-3).
%F A117867 a(n) = (1/(4*sqrt(2)))*( -8*sqrt(2) + 9*(1 - (-1)^n)*2^(3*n/2) + (1 + (-1)^n)*2^((3*n+5)/2) ).
%F A117867 E.g.f.: 2*cosh(2*sqrt(2)*x) + (9/(2*sqrt(2)))*sinh(2*sqrt(2)*x) -2*cosh(x) - 2*sinh(x). (End)
%t A117867 Table[If[OddQ[n],9*8^((n-1)/2)-2, 2*8^(n/2)-2], {n,1,25}] (* or *) LinearRecurrence[{1,8,-8}, {7,14,70}, 25] (* _G. C. Greubel_, Oct 27 2016 *)
%t A117867 Rest@ CoefficientList[Series[7 x (x + 1)/((x - 1) (8 x^2 - 1)), {x, 0, 27}], x] (* _Michael De Vlieger_, Oct 27 2016 *)
%Y A117867 Cf. A050250.
%K A117867 nonn,base,easy
%O A117867 1,1
%A A117867 _Martin Renner_, May 02 2006
%E A117867 More terms from _Colin Barker_, Feb 15 2013