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 A163207 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
 1, 29, 812, 22736, 636202, 17802288, 498146166, 13939191504, 390048294510, 10914382803996, 305407698579522, 8545958486918244, 239134137088822794, 6691482951706744632, 187241958166564053774, 5239429159586654676168 (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, -378). FORMULA G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^4 - 27*t^3 - 27*t^2 - 27*t + 1). From G. C. Greubel, Apr 28 2019: (Start) a(n) = 27*(a(n-1) + a(n-2) + a(n-3) -14*a(n-4)). G.f.: (1+x)*(1-x^4)/(1 - 28*x + 405*x^4 - 378*x^5). (End) MATHEMATICA CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(378*t^4-27*t^3-27*t^2 - 27*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{27, 27, 27, -378}, {1, 29, 812, 22736, 636202}, 20] (* G. C. Greubel, Dec 10 2016 *) coxG[{4, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5) )); // G. C. Greubel, Apr 28 2019 (Sage) ((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019 (GAP) a:=[29, 812, 22736, 636202];; for n in [5..20] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3] -14*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019 CROSSREFS Sequence in context: A180844 A159669 A162831 * A163549 A164026 A164665 Adjacent sequences:  A163204 A163205 A163206 * A163208 A163209 A163210 KEYWORD nonn,easy AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)