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 A163519 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
 1, 24, 552, 12696, 292008, 6715908, 154459536, 3552423600, 81702391056, 1879077904176, 43217018799372, 993950655137880, 22859927229943848, 525756756894338904, 12091909332851083560, 278102505382114851108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170743, 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..730 Index entries for linear recurrences with constant coefficients, signature (22, 22, 22, 22, -253). FORMULA G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1). a(n) = 22*a(n-1)+22*a(n-2)+22*a(n-3)+22*a(n-4)-253*a(n-5). - Wesley Ivan Hurt, May 10 2021 MATHEMATICA CoefficientList[Series[(1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *) coxG[{5, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 16 2018 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)) \\ G. C. Greubel, Jul 27 2017 (Magma) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6) )); // G. C. Greubel, May 16 2019 (Sage) ((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019 CROSSREFS Sequence in context: A334673 A342888 A163174 * A163992 A164637 A164959 Adjacent sequences: A163516 A163517 A163518 * A163520 A163521 A163522 KEYWORD nonn,easy AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)