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 A248169 #8 Sep 30 2019 06:43:09
%S A248169 1,2,6,18,46,146,398,1234,3454,10610,30230,92290,265670,808210,
%T A248169 2343182,7110994,20720798,62774578,183617910,555559554,1629845726,
%U A248169 4926370114,14486707710,43752525762,128909169334,389075915954,1148184115062,3463595977986,10235096852902
%N A248169 G.f.: AGM( (1-x)/(1+x), (1+3*x)/(1-3*x) ).
%C A248169 Here AGM(x,y) = AGM((x+y)/2,sqrt(x*y)) is the arithmetic-geometric mean.
%C A248169 a(n) == 2 (mod 4) for n>0.
%C A248169 Limit a(n+1)/a(n) = 3.
%H A248169 Vaclav Kotesovec, <a href="/A248169/b248169.txt">Table of n, a(n) for n = 0..1000</a>
%F A248169 a(n) ~ Pi * 3^n / log(n) * (1 - (gamma + 4*log(2))/log(n) + (gamma^2 + 8*log(2)*gamma + 16*log(2)^2 - Pi^2/6) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Sep 30 2019
%e A248169 G.f.: A(x) = 1 + 2*x + 6*x^2 + 18*x^3 + 46*x^4 + 146*x^5 + 398*x^6 +...
%t A248169 CoefficientList[Series[Pi*(1 + 3*x)/((2*(1 - 3*x)*EllipticK[(16*x*(1 + 3*x^2)) / ((1 + x)^2*(1 + 3*x)^2)])), {x, 0, 30}], x] (* _Vaclav Kotesovec_, Sep 26 2019 *)
%o A248169 (PARI) {a(n)=local(A,X=x+x*O(x^n));A=agm((1-x)/(1+X),(1+3*x)/(1-3*X)); polcoeff(A,n)}
%o A248169 for(n=0,40,print1(a(n),", "))
%Y A248169 Cf. A063887.
%K A248169 nonn
%O A248169 0,2
%A A248169 _Paul D. Hanna_, Oct 03 2014