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A168710 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168710 #13 Aug 04 2020 12:54:21
%S A168710 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A168710 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A168710 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A168710 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168710 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A168710 First disagreement at index 17: a(17) = 39894552047282762765303280, A170752(17) = 39894552047282762765303808. - _Klaus Brockhaus_, Mar 28 2011
%C A168710 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168710 G. C. Greubel, <a href="/A168710/b168710.txt">Table of n, a(n) for n = 0..500</a>
%H A168710 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A168710 G.f.: (t^17 + 2*t^16 + 2*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)/(496*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%t A168710 CoefficientList[Series[(t^17 + 2*t^16 + 2*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)/(496*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%t A168710 coxG[{17,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 04 2020 *)
%Y A168710 Cf. A170752 (G.f.: (1+x)/(1-32*x)).
%K A168710 nonn
%O A168710 0,2
%A A168710 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009