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Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
0

%I #12 May 27 2018 14:16:50

%S 1,35,1190,40460,1375640,46771760,1590239245,54068114100,

%T 1838315192175,62502693168300,2125090773290100,72253059281172000,

%U 2456603097196693830,83524474080352031265,2839831057104956921160,96554219846263616159415

%N Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%C The initial terms coincide with those of A170754, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, -561).

%F G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

%t CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Sep 09 2017 *)

%t coxG[{6,561,-33}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 27 2018 *)

%o (PARI) t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)) \\ _G. C. Greubel_, Sep 09 2017

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009