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 A164697 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I. 1
 1, 4, 12, 36, 108, 324, 972, 2916, 8742, 26208, 78576, 235584, 706320, 2117664, 6349104, 19035648, 57071982, 171111132, 513019140, 1538115228, 4611520836, 13826093148, 41452886916, 124282529820, 372619336494, 1117173669768 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A003946, although the two sequences are eventually different. Computed with MAGMA using commands similar to those used to compute A154638. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,2,-3). FORMULA G.f.: (x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/( 3*x^8 - 2*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - 2*x^2 - 2*x + 1). MAPLE seq(coeff(series((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 16 2019 MATHEMATICA CoefficientList[Series[(x^8 +2x^7 +2x^6 +2x^5 +2x^4 +2x^3 +2x^2 +2x +1)/( 3x^8 -2x^7 -2x^6 -2x^5 -2x^4 -2x^3 -2x^2 -2x +1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *) coxG[{8, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 03 2019 *) PROG (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)) \\ G. C. Greubel, Sep 16 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9) )); // G. C. Greubel, Sep 16 2019 (Sage) def A164697_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)).list() A164697_list(30) # G. C. Greubel, Sep 16 2019 (GAP) a:=[4, 12, 36, 108, 324, 972, 2916, 8742];; for n in [9..30] do a[n]:=2*Sum([1..7], j-> a[n-j]) -3*a[n-8]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019 CROSSREFS Sequence in context: A163877 A336262 A164353 * A165184 A165756 A166328 Adjacent sequences:  A164694 A164695 A164696 * A164698 A164699 A164700 KEYWORD nonn,easy AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified May 6 02:46 EDT 2021. Contains 343579 sequences. (Running on oeis4.)