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 A163221 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
 1, 38, 1406, 52022, 1924111, 71166096, 2632183848, 97355219328, 3600827035866, 133181923185576, 4925930761424952, 182192847843197736, 6738672428195210748, 249239784283952410080, 9218502714272560450272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A170757, 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..635 Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, -666). FORMULA G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^4 - 36*t^3 - 36*t^2 - 36*t + 1). a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)-666*a(n-4). - Wesley Ivan Hurt, May 06 2021 MATHEMATICA coxG[{4, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2015 *) CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3-36*t^2 - 36*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{36, 36, 36, -666}, {1, 38, 1406, 52022, 1924111}, 20] (* G. C. Greubel, Dec 11 2016; modified by Georg Fischer, Apr 08 2019 *) PROG (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3 - 36*t^2-36*t+1)) \\ G. C. Greubel, Dec 11 2016 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5) )); // G. C. Greubel, May 01 2019 (Sage) ((1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019 (GAP) a:=[38, 1406, 52022, 1924111];; for n in [5..20] do a[n]:=36*(a[n-1]+ a[n-2]+a[n-3]) -666*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019 CROSSREFS Sequence in context: A027657 A268885 A162858 * A163660 A164071 A164674 Adjacent sequences:  A163218 A163219 A163220 * A163222 A163223 A163224 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified January 24 04:47 EST 2022. Contains 350534 sequences. (Running on oeis4.)