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A168798 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168798 #16 Jan 02 2022 13:48:26
%S A168798 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A168798 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A168798 913008685901414400,21912208461633945600,525893003079214694400
%N A168798 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168798 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A168798 First disagreement at index 19: a(19) = 174478676989609534449254100, A170744(19) = 174478676989609534449254400. - _Klaus Brockhaus_, Apr 01 2011
%C A168798 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168798 G. C. Greubel, <a href="/A168798/b168798.txt">Table of n, a(n) for n = 0..500</a>
%H A168798 <a href="/index/Rec#order_19">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, 23, 23, -276).
%F A168798 G.f.: (t^19 + 2*t^18 + 2*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^19 - 23*t^18 - 23*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 A168798 CoefficientList[Series[(t^19 + 2*t^18 + 2*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^19 - 23*t^18 - 23*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 16 2016 *)
%t A168798 coxG[{19,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 02 2022 *)
%Y A168798 Cf. A170744 (G.f.: (1+x)/(1-24*x)).
%K A168798 nonn
%O A168798 0,2
%A A168798 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009