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 A163668 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
 1, 39, 1482, 56316, 2140008, 81319563, 3090115236, 117423309705, 4462045136796, 169556171182476, 6443075832883092, 244834652131935645, 9303632060115383718, 353534798919570074859, 13434200024194718979990 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170758, 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..630 Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, -703). FORMULA G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1). MATHEMATICA CoefficientList[Series[(1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *) coxG[{5, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 23 2019 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)) \\ G. C. Greubel, Aug 01 2017 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6) )); // G. C. Greubel, May 23 2019 (Sage) ((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 23 2019 (GAP) a:=[39, 1482, 56316, 2140008, 81319563];; for n in [6..20] do a[n]:=37*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -703*a[n-5]; od; Concatenation(, a); # G. C. Greubel, May 23 2019 CROSSREFS Sequence in context: A097314 A162871 A163222 * A164084 A164681 A165171 Adjacent sequences:  A163665 A163666 A163667 * A163669 A163670 A163671 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified September 20 17:13 EDT 2020. Contains 337265 sequences. (Running on oeis4.)