cp's OEIS Frontend

A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

%I A164681 #15 Sep 08 2022 08:45:47
%S A164681 1,39,1482,56316,2140008,81320304,3090171552,117426518235,
%T A164681 4462207664772,169563890192073,6443427786666780,244850254349321868,
%U A164681 9304309606601631648,353563762821303227856,13435422902486289765684
%N A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164681 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A164681 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164681 Vincenzo Librandi, <a href="/A164681/b164681.txt">Table of n, a(n) for n = 0..200</a>
%H A164681 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, -703).
%F A164681 G.f.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(703*x^7 - 37*x^6 - 37*x^5 - 37*x^4 - 37*x^3 - 37*x^2 - 37*x + 1).
%F A164681 G.f.: (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8). - _G. C. Greubel_, Apr 26 2019
%t A164681 CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(703 x^7 - 37 x^6 - 37 x^5 - 37 x^4 - 37 x^3 - 37 x^2 - 37 x + 1), {x, 0, 20}], x ] (* _Vincenzo Librandi_, Apr 29 2014 *)
%t A164681 coxG[{7, 703, -37}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)
%o A164681 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-38*x+740*x^7-703*x^8)) \\ _G. C. Greubel_, Apr 26 2019
%o A164681 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8) )); // _G. C. Greubel_, Apr 26 2019
%o A164681 (Sage) ((1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%K A164681 nonn,easy
%O A164681 0,2
%A A164681 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009