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 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. 2
 1, 1, 3, 10, 35, 126, 462, 1717, 6451, 24463, 93518, 360031, 1394582, 5430530, 21242341, 83411715, 328589491, 1297937234, 5138431851, 20380608990, 80960325670, 322016144629, 1282138331587, 5109310929719, 20374764059254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 134. Index entries for linear recurrences with constant coefficients, signature (9,-26,25,-4). FORMULA G.f.: (1-8*x+20*x^2-16*x^3+2*x^4)/(1-9*x+26*x^2-25*x^3+4*x^4). - Michael Somos, Jul 21, 2002 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 EXAMPLE The words tttt=tsts=stst=1 so a(2)=3. MATHEMATICA LinearRecurrence[{9, -26, 25, -4}, {1, 1, 3, 10, 35}, 30] (* Harvey P. Dale, Apr 16 2022 *) PROG (PARI) a(n)=if(n<1, n==0, sum(k=-(n-1)\7, (n-1)\7, C(2*n-1, n+7*k))) (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 CROSSREFS Sequence in context: A001700 A088218 A300975 * A085282 A149036 A316596 Adjacent sequences: A072263 A072264 A072265 * A072267 A072268 A072269 KEYWORD nonn,easy AUTHOR Jamaine Paddyfoot (jay_paddyfoot(AT)hotmail.com) and John W. Layman, Jul 08 2002 STATUS approved

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Last modified August 6 18:55 EDT 2024. Contains 374981 sequences. (Running on oeis4.)