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 A164026 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I. 1
 1, 29, 812, 22736, 636608, 17825024, 499100266, 13974796080, 391293972342, 10956222324432, 306773975852064, 8589664345360896, 240510406272356430, 6734285904493468188, 188559852134231228994, 5279671570397554562148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170748, 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..685 Index entries for linear recurrences with constant coefficients, signature (27,27,27,27,27,-378). FORMULA G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1). a(n) = -378*a(n-6) + 27*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021 MAPLE seq(coeff(series((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019 MATHEMATICA CoefficientList[Series[(1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *) coxG[{6, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 14 2019 *) PROG (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)) \\ G. C. Greubel, Sep 07 2017 (MAGMA) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7) )); // G. C. Greubel, Aug 13 2019 (Sage) def A164026_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)).list() A164026_list(30) # G. C. Greubel, Aug 13 2019 (GAP) a:=[29, 812, 22736, 636608, 17825024, 499100266];; for n in [7..30] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -378*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019 CROSSREFS Sequence in context: A162831 A163207 A163549 * A164665 A164974 A165512 Adjacent sequences:  A164023 A164024 A164025 * A164027 A164028 A164029 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified July 30 23:02 EDT 2021. Contains 346365 sequences. (Running on oeis4.)