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A168788 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168788 #14 Jun 24 2021 18:38:12
%S A168788 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A168788 309915701760,4338819824640,60743477544960,850408685629440,
%U A168788 11905721598812160,166680102383370240,2333521433367183360
%N A168788 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168788 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A168788 First disagreement at index 19: a(19) = 6403182813159551139735, A170734(19) = 6403182813159551139840. - _Klaus Brockhaus_, Mar 30 2011
%C A168788 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168788 G. C. Greubel, <a href="/A168788/b168788.txt">Table of n, a(n) for n = 0..500</a>
%H A168788 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A168788 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)/(91*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%t A168788 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)/(91*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 15 2016 *)
%t A168788 coxG[{19,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 24 2021 *)
%Y A168788 Cf. A170734 (G.f.: (1+x)/(1-14*x)).
%K A168788 nonn
%O A168788 0,2
%A A168788 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009