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 A026743 #22 Mar 08 2023 05:33:38
%S A026743 1,2,4,8,17,34,73,146,314,628,1350,2700,5798,11596,24872,49744,106573,
%T A026743 213146,456169,912338,1950697,3901394,8334539,16669078,35582783,
%U A026743 71165566,151809737,303619474,647279131,1294558262,2758310121
%N A026743 a(n) = Sum_{j=0..n} T(n,j), T given by A026736.
%H A026743 G. C. Greubel, <a href="/A026743/b026743.txt">Table of n, a(n) for n = 0..1000</a>
%F A026743 G.f.: ((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1 -4*x^2 - x^4)). - _David Callan_, Jan 17 2016
%F A026743 Conjecture D-finite with recurrence n*a(n) -2*a(n-1) +(-11*n+20)*a(n-2) +14*a(n-3) +(39*n-152)*a(n-4) -22*a(n-5) +(-41*n+268)*a(n-6) -6*a(n-7) +12*(-n+6)*a(n-8)=0. - _R. J. Mathar_, Jan 13 2023
%F A026743 a(n) ~ ((1 + (-1)^n)*phi^(3/2) + 2*(1 - (-1)^n)) * phi^((3*n + 1)/2) / (2*sqrt(5)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Mar 08 2023
%t A026743 CoefficientList[Normal[Series[((1-3x^2)Sqrt[(1+2x)/(1-2x)] +(1 + 2x)(1+ x^2))/(2(1-4x^2-x^4)), {x,0,40}]], x] (* _David Callan_, Jan 17 2016 *)
%o A026743 (PARI) my(x='x+O('x^40)); Vec(((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4))) \\ _G. C. Greubel_, Jul 16 2019
%o A026743 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( ((1 -3*x^2)*Sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4)) )); // _G. C. Greubel_, Jul 16 2019
%o A026743 (Sage) (((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1-4*x^2 - x^4))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 16 2019
%Y A026743 Cf. A026736.
%K A026743 nonn
%O A026743 0,2
%A A026743 _Clark Kimberling_