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 A164050 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
 1, 34, 1122, 37026, 1221858, 40321314, 1330602801, 43909873920, 1449025228992, 47817812414592, 1577987144990784, 52073553849901056, 1718426553198820080, 56708052368589946368, 1871364939893753424384, 61755017003604231740928 (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 (32,32,32,32,32,-528). FORMULA G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1). a(n) = -528*a(n-6) + 32*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021 MAPLE seq(coeff(series((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019 MATHEMATICA CoefficientList[Series[(1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 08 2017 *) LinearRecurrence[{32, 32, 32, 32, 32, -528}, {1, 34, 1122, 37026, 1221858, 40321314, 1330602801}, 21]] (* Vincenzo Librandi, Sep 09 2017 *) coxG[{6, 528, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *) PROG (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)) \\ G. C. Greubel, Sep 08 2017 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7) )); // G. C. Greubel, Aug 13 2019 (Sage) def A164050_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)).list() A164050_list(30) # G. C. Greubel, Aug 13 2019 (GAP) a:=[34, 1122, 37026, 1221858, 40321314, 1330602801];; for n in [7..30] do a[n]:=32*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -528*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019 CROSSREFS Sequence in context: A162838 A163217 A163593 * A164670 A165166 A165649 Adjacent sequences: A164047 A164048 A164049 * A164051 A164052 A164053 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified September 21 11:30 EDT 2023. Contains 365501 sequences. (Running on oeis4.)