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 A163593 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
 1, 34, 1122, 37026, 1221858, 40320753, 1330566336, 43908078720, 1448946455616, 47814568344576, 1577858820890352, 52068617261591040, 1718240483647446528, 56701147733816154624, 1871111864101388705280, 61745833160498214613248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170753, although the two sequences are eventually different. Computed with MAGMA using commands similar to those used to compute A154638. LINKS G. C. Greubel, Table of n, a(n) for n = 0..655 Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, 32, -528). FORMULA G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1). a(n) = 32*a(n-1)+32*a(n-2)+32*a(n-3)+32*a(n-4)-528*a(n-5). - Wesley Ivan Hurt, May 11 2021 MATHEMATICA coxG[{5, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 04 2016 *) CoefficientList[Series[(1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)) \\ G. C. Greubel, Jul 29 2017 (Magma) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6) )); // G. C. Greubel, Apr 28 2019 (Sage) ((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019 CROSSREFS Sequence in context: A214241 A162838 A163217 * A164050 A164670 A165166 Adjacent sequences: A163590 A163591 A163592 * A163594 A163595 A163596 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified September 13 05:16 EDT 2024. Contains 375859 sequences. (Running on oeis4.)