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%I A167108 #11 Jun 08 2018 17:42:16
%S A167108 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A167108 423263232,2539579392,15237476352,91424858091,548549148420,
%U A167108 3291294889785,19747769334300,118486615979340,710919695717280,4265518173351120
%N A167108 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
%C A167108 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A167108 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167108 G. C. Greubel, <a href="/A167108/b167108.txt">Table of n, a(n) for n = 0..500</a>
%H A167108 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
%F A167108 G.f.: (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)/(15*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%t A167108 CoefficientList[Series[(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)/ (15*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 03 2016 *)
%t A167108 coxG[{14,15,-5}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 08 2018 *)
%K A167108 nonn
%O A167108 0,2
%A A167108 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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