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A168702 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168702 #13 Aug 03 2019 13:45:04
%S A168702 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A168702 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A168702 913008685901414400,21912208461633945600,525893003079214694400
%N A168702 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168702 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A168702 First disagreement at index 17: a(17) = 302914369773627663974100, A170744(17) = 302914369773627663974400. - _Klaus Brockhaus_, Mar 30 2011
%C A168702 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168702 G. C. Greubel, <a href="/A168702/b168702.txt">Table of n, a(n) for n = 0..500</a>
%H A168702 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
%F A168702 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)/(276*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
%t A168702 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)/(276*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)
%t A168702 coxG[{17,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 03 2019 *)
%Y A168702 Cf. A170744 (G.f.: (1+x)/(1-24*x)).
%K A168702 nonn
%O A168702 0,2
%A A168702 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009