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 A099854 #12 Apr 21 2023 02:07:10
%S A099854 1,3,7,14,26,48,90,170,321,605,1139,2144,4037,7603,14319,26966,50782,
%T A099854 95632,180094,339154,638697,1202797,2265111,4265664,8033113,15127987,
%U A099854 28489079,53650734,101035250,190269936,358317010,674783850,1270755313
%N A099854 A Chebyshev transform of A048739 related to the knot 8_5.
%C A099854 The g.f. is a transformation of the g.f. 1/((1-x)*(1-2*x-x^2)) of A048739 under the Chebyshev transform G(x)->(1/(1+x^2))*G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial of the knot 8_5.
%H A099854 G. C. Greubel, <a href="/A099854/b099854.txt">Table of n, a(n) for n = 0..1000</a>
%H A099854 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,5,-4,3,-1).
%F A099854 G.f.: (1 + x^2)^2/(1 - 3*x + 4*x^2 - 5*x^3 + 4*x^4 - 3*x^5 + x^6).
%F A099854 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*A048739(n-2*k).
%F A099854 a(n) = Sum_{k=0..n} A099846(n-k)*binomial(2, k/2)*(1+(-1)^k)/2.
%F A099854 a(n) = (1/2)*(3*A112575(n+1) + A112575(n) + 3*A112575(n-1) - A010892(n)). - _G. C. Greubel_, Apr 20 2023
%t A099854 LinearRecurrence[{3,-4,5,-4,3,-1}, {1,3,7,14,26,48}, 51] (* _G. C. Greubel_, Apr 20 2023 *)
%o A099854 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^2)^2/((1-x+x^2)*(1-2*x+x^2-2*x^3+x^4)) )); // _G. C. Greubel_, Apr 20 2023
%o A099854 (SageMath)
%o A099854 def A099854_list(prec):
%o A099854 P.<x> = PowerSeriesRing(ZZ, prec)
%o A099854 return P( (1+x^2)^2/((1-x+x^2)*(1-2*x+x^2-2*x^3+x^4)) ).list()
%o A099854 A099854_list(50) # _G. C. Greubel_, Apr 20 2023
%Y A099854 Cf. A010892, A048739, A099846, A112575.
%K A099854 easy,nonn
%O A099854 0,2
%A A099854 _Paul Barry_, Oct 27 2004