cp's OEIS Frontend

A166171 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166171 #12 Mar 11 2020 21:26:24
%S A166171 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A166171 4462207721088,169563893401344,6443427949250331,244850262071484420,
%U A166171 9304309958715338697,353563778431142238492,13435423580381861046924
%N A166171 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166171 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A166171 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166171 G. C. Greubel, <a href="/A166171/b166171.txt">Table of n, a(n) for n = 0..500</a>
%H A166171 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A166171 G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%p A166171 seq(coeff(series((1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166171 CoefficientList[Series[(1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)
%t A166171 coxG[{703, 10, -37}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166171 (Sage)
%o A166171 def A166171_list(prec):
%o A166171     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166171     return P( (1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11) ).list()
%o A166171 A166171_list(30) # _G. C. Greubel_, Aug 10 2019
%K A166171 nonn
%O A166171 0,2
%A A166171 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009