cp's OEIS Frontend

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.

A099455 An Alexander sequence for the knot 8_12.

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%I A099455 #22 May 13 2024 17:23:38
%S A099455 1,7,36,168,755,3346,14747,64848,284892,1251103,5493314,24118255,
%T A099455 105887532,464877504,2040939083,8960260498,39337870403,172703402424,
%U A099455 758212386132,3328747303735,14614056052994,64159460722903,281676515111412,1236632261449368,5429133302704547
%N A099455 An Alexander sequence for the knot 8_12.
%C A099455 The denominator is a parameterization of the Alexander polynomial for the knot 8_12. 1/(1-7*x+13*x^2-7*x^3+x^4) is the image of the g.f. of A099453 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2)).
%H A099455 Stefano Spezia, <a href="/A099455/b099455.txt">Table of n, a(n) for n = 0..1500</a>
%H A099455 Dror Bar-Natan, <a href="http://katlas.org/wiki/Main_Page">The Rolfsen Knot Table</a>.
%H A099455 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-13,7,-1).
%F A099455 G.f.: (1-x)*(1+x)*(1+x^2)/(1-7*x+13*x^2-7*x^3+x^4). - corrected Nov 24 2012
%F A099455 a(n) = A099454(n) - A099454(n-2).
%t A099455 LinearRecurrence[{7,-13,7,-1},{1,7,36,168,755},30] (* _Harvey P. Dale_, Jan 31 2017 *)
%Y A099455 Cf. A099454.
%K A099455 easy,nonn
%O A099455 0,2
%A A099455 _Paul Barry_, Oct 16 2004