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 A072266 #18 Jul 04 2025 17:23:21
%S A072266 1,1,3,10,35,126,462,1717,6451,24463,93518,360031,1394582,5430530,
%T A072266 21242341,83411715,328589491,1297937234,5138431851,20380608990,
%U A072266 80960325670,322016144629,1282138331587,5109310929719,20374764059254
%N A072266 Number of words of length 2n generated by the two letters s and t that reduce to the identity 1 using the relations sssssss=1, tt=1 and stst=1. The generators s and t along with the three relations generate the 14-element dihedral group D7.
%H A072266 Colin Barker, <a href="/A072266/b072266.txt">Table of n, a(n) for n = 0..1000</a>
%H A072266 H. S. M. Coxeter and W. O. J. Moser, <a href="http://doi.org/10.1007/978-3-662-21943-0">Generators and Relations for Discrete Groups</a>, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 134.
%H A072266 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,25,-4).
%F A072266 G.f.: 1 -x*(2*x-1)*(x^2-4*x+1)/((4*x-1)*(x^3-6*x^2+5*x-1)). - _Michael Somos_, Jul 21 2002
%F A072266 a(n) = 9*a(n-1) - 26*a(n-2) + 25*a(n-3) - 4*a(n-4) for n>4. - _Colin Barker_, Apr 26 2019
%F A072266 14*a(n) = 4^n +2*(3*A005021(n) -10*A005021(n-1) +6*A005021(n-2)), n>0. - _R. J. Mathar_, Nov 05 2024
%e A072266 The words tttt=tsts=stst=1 so a(2)=3.
%t A072266 LinearRecurrence[{9,-26,25,-4},{1,1,3,10,35},30] (* _Harvey P. Dale_, Apr 16 2022 *)
%o A072266 (PARI) a(n)=if(n<1,n==0,sum(k=-(n-1)\7,(n-1)\7,C(2*n-1,n+7*k)))
%o A072266 (PARI) Vec((1 - 8*x + 20*x^2 - 16*x^3 + 2*x^4) / ((1 - 4*x)*(1 - 5*x + 6*x^2 - x^3)) + O(x^30)) \\ _Colin Barker_, Apr 26 2019
%Y A072266 Bisection of A377573.
%K A072266 nonn,easy
%O A072266 0,3
%A A072266 Jamaine Paddyfoot (jay_paddyfoot(AT)hotmail.com) and _John W. Layman_, Jul 08 2002