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 A167205 #40 Mar 05 2018 08:52:06
%S A167205 1,1,5,7,41,61,365,547,3281,4921,29525,44287,265721,398581,2391485,
%T A167205 3587227,21523361,32285041,193710245,290565367,1743392201,2615088301,
%U A167205 15690529805,23535794707,141214768241,211822152361,1270932914165
%N A167205 a(n) = (3^n+1)/(3-(-1)^n).
%C A167205 This sequence is (3^n + 1) divided by the highest possible power of 2, which is 4 for odd n and 2 for even n. It is never divisible by 8 or any higher power of 2, which implies Levi ben Gerson's observation that (3^n + 1 = 2^k) has no solution for n > 1. Cf. the comments and links to A235365. - _Joe Slater_, Apr 02 2017
%H A167205 G. C. Greubel, <a href="/A167205/b167205.txt">Table of n, a(n) for n = 0..1000</a>
%H A167205 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10,0,-9)
%F A167205 a(n) = 10*a(n-2) - 9*a(n-4).
%F A167205 G.f.: (1 + x - 5*x^2 - 3*x^3)/((1+x)*(1-x)*(1+3*x)*(1-3*x)).
%F A167205 a(n) = numerator((1/4)^n + (3/4)^n), n > 0.
%p A167205 a:=n->(3^n+1)/(3-(-1)^n): seq(a(n),n=0..27); # _Muniru A Asiru_, Mar 05 2018
%t A167205 CoefficientList[Series[(1+x-5x^2-3x^3)/((1+x)(1-x)(1+3x)(1-3x)), {x,0,30}],x] (* or *) LinearRecurrence[{0,10,0,-9},{1,1,5,7},30] (* _Harvey P. Dale_, Apr 25 2011 *)
%o A167205 (PARI) a(n) = (3^n+1)/(3-(-1)^n); \\ _Altug Alkan_, Mar 05 2018
%o A167205 (GAP) List([0..27],n->(3^n+1)/(3-(-1)^n)); # _Muniru A Asiru_, Mar 05 2018
%Y A167205 Cf. A007051, A074476, A235365.
%K A167205 nonn,easy
%O A167205 0,3
%A A167205 _Jaume Oliver Lafont_, Oct 30 2009