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A167818 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%I A167818 #22 Apr 12 2019 12:44:52
%S A167818 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A167818 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A167818 4870003042163884032,175320109517899825152,6311523942644393705472
%N A167818 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.
%C A167818 The initial terms coincide with those of A170756, although the two sequences start to be different at a(15).
%C A167818 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167818 G. C. Greubel, <a href="/A167818/b167818.txt">Table of n, a(n) for n = 0..500</a>
%H A167818 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A167818 G.f.: (t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/(630*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
%p A167818 (t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/(630*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1);
%p A167818 taylor(%,t=0,64) ;
%p A167818 gfun[seriestolist](%) ; # _R. J. Mathar_, Apr 12 2019
%t A167818 coxG[{15,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 19 2014 *)
%t A167818 CoefficientList[Series[(t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/(630*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 27 2016 *)
%K A167818 nonn
%O A167818 0,2
%A A167818 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
%E A167818 Programs and 500-term b-file confirmed by _Robert Israel_ and _Vaclav Kotesovec_, Apr 11 2019