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A168782 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168782 #18 Apr 26 2018 05:08:27
%S A168782 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A168782 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A168782 316659348799488,2533274790395904,20266198323167232,162129586585337820
%N A168782 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168782 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A168782 First disagreement at index 19: a(19) = 162129586585337820, A003951(19) = 162129586585337856. - _Klaus Brockhaus_, Mar 25 2011
%C A168782 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168782 G. C. Greubel, <a href="/A168782/b168782.txt">Table of n, a(n) for n = 0..500</a>
%H A168782 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A168782 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)/(28*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%t A168782 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)/(28*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%t A168782 coxG[{19,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 26 2018 *)
%Y A168782 Cf. A003951 (G.f.: (1+x)/(1-8*x)).
%K A168782 nonn,easy
%O A168782 0,2
%A A168782 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009