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 A173993 #21 Aug 18 2024 20:10:41
%S A173993 1,2,6,17,50,146,430,1267,3746,11091,32900,97716,290586,864980,
%T A173993 2577032,7683397,22922874,68427057,204362172,610604629,1825092080,
%U A173993 5457016431,16321318264,48828168580,146112907266,437319580738,1309158060068
%N A173993 Sequence whose Hankel transform is the Somos (4) sequence.
%C A173993 Hankel transform is A006720(n+3).
%H A173993 G. C. Greubel, <a href="/A173993/b173993.txt">Table of n, a(n) for n = 0..1000</a>
%F A173993 G.f.: (sqrt((1-2x)*(1-2x-4x^2+4x^3))-2x^2+4x-1)/(2x*(1-4x+3x^2)).
%F A173993 Conjecture: (n+1)*a(n) +2*(-4*n-1)*a(n-1) +(19*n-5)*a(n-2) -36*a(n-3) +8*(-7*n+26)*a(n-4) +2*(34*n-143)*a(n-5) +24*(-n+5)*a(n-6)=0. - _R. J. Mathar_, Oct 10 2014
%t A173993 CoefficientList[Series[(Sqrt[(1-2*x)*(1-2*x-4*x^2+4*x^3)]-2*x^2+4*x-1)/( 2 x*(1 - 4 x + 3 x^2)), {x, 0, 50}], x] (* _G. C. Greubel_, Sep 22 2018 *)
%o A173993 (PARI) my(x='x+O('x^50)); Vec((sqrt((1-2*x)*(1-2*x-4*x^2+4*x^3))-2*x^2+4*x-1)/(2*x*(1-4*x+3*x^2))) \\ _G. C. Greubel_, Sep 22 2018
%o A173993 (Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((Sqrt((1-2*x)*(1-2*x-4*x^2+4*x^3))-2*x^2+4*x-1)/(2*x*(1-4*x+3*x^2)))); // _G. C. Greubel_, Sep 22 2018
%Y A173993 Cf. A006720, A173992.
%K A173993 easy,nonn
%O A173993 0,2
%A A173993 _Paul Barry_, Mar 04 2010