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 A099449 #23 Apr 06 2025 07:39:18
%S A099449 1,5,18,60,197,650,2153,7140,23682,78545,260498,863945,2865282,
%T A099449 9502740,31515953,104523050,346651997,1149675660,3812913618,
%U A099449 12645575405,41939208002,139091904605,461300030418,1529907284460,5073956524397
%N A099449 An Alexander sequence for the knot 7_6.
%C A099449 The denominator is a parameterization of the Alexander polynomial for the knot 7_6. The g.f. is the image of the g.f. of A030191 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2))
%H A099449 Vincenzo Librandi, <a href="/A099449/b099449.txt">Table of n, a(n) for n = 0..1000</a>
%H A099449 <a href="https://katlas.org/wiki/The_Rolfsen_Knot_Table">The Rolfsen Knot Table</a>
%H A099449 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,5,-1).
%F A099449 G.f.: -(x-1)*(x+1)*(x^2+1) / (x^4-5*x^3+7*x^2-5*x+1). - _Colin Barker_, Feb 10 2014
%F A099449 a(n) = A099448(n) - A099448(n-2).
%F A099449 a(n) = 5*a(n-1)-7*a(n-2)+5*a(n-3)-a(n-4) for n>4. - _Colin Barker_, Feb 10 2014
%t A099449 CoefficientList[Series[(1 - x) (x + 1) (x^2 + 1)/(x^4 -5 x^3 + 7 x^2 - 5 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 12 2014 *)
%t A099449 LinearRecurrence[{5,-7,5,-1},{1,5,18,60,197},30] (* _Harvey P. Dale_, Oct 06 2015 *)
%o A099449 (PARI) Vec(-(x-1)*(x+1)*(x^2+1)/(x^4-5*x^3+7*x^2-5*x+1) + O(x^100)) \\ _Colin Barker_, Feb 10 2014
%o A099449 (Magma) I:=[1,5,18,60,197,650,2153,7140]; [n le 8 select I[n] else 5*Self(n-1)-7*Self(n-2)+5*Self(n-3)-Self(n-4) : n in [1..30]]; // _Vincenzo Librandi_, Feb 12 2014
%Y A099449 Cf. A030191, A099448.
%K A099449 easy,nonn
%O A099449 0,2
%A A099449 _Paul Barry_, Oct 16 2004
%E A099449 G.f. corrected by _Colin Barker_, Feb 10 2014