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 A162871 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I. 1
 1, 39, 1482, 55575, 2083692, 78111033, 2928135600, 109766289945, 4114781688966, 154249795892907, 5782323668697966, 216760526662519203, 8125647855742321632, 304604136609884440797, 11418619374984439210164 (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..615 Index entries for linear recurrences with constant coefficients, signature (37, 37, -703). FORMULA G.f.: (t^3 + 2*t^2 + 2*t + 1)/(703*t^3 - 37*t^2 - 37*t + 1). a(n) = 37*a(n-1) + 37*a(n-2) - 703*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018 G.f.: (1+x)*(1-x^3)/(1 - 38*x + 740*x^3 - 703*x^4). - G. C. Greubel, Apr 27 2019 MAPLE seq(coeff(series((x^3+2*x^2+2*x+1)/(703*x^3-37*x^2-37*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018 MATHEMATICA coxG[{3, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 25 2018 *) CoefficientList[Series[(t^3+2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *) PROG (PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1)) \\ G. C. Greubel, Oct 24 2018 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1))); // G. C. Greubel, Oct 24 2018 (GAP) a:=[39, 1482, 55575];; for n in [4..15] do a[n]:=37*a[n-1]+37*a[n-2]-703*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018 (Sage) ((1+x)*(1-x^3)/(1 -38*x +740*x^3 -703*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019 CROSSREFS Sequence in context: A020303 A235973 A097314 * A163222 A163668 A164084 Adjacent sequences:  A162868 A162869 A162870 * A162872 A162873 A162874 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified August 4 20:00 EDT 2020. Contains 336202 sequences. (Running on oeis4.)