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A168783 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168783 #18 Nov 24 2016 16:16:12
%S A168783 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A168783 34867844010,313810596090,2824295364810,25418658283290,
%U A168783 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A168783 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168783 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A168783 First disagreement at index 19: a(19) = 1500946352969991165, A003952(19) = 1500946352969991210. - _Klaus Brockhaus_, Mar 25 2011
%C A168783 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168783 G. C. Greubel, <a href="/A168783/b168783.txt">Table of n, a(n) for n = 0..500</a>
%H A168783 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).
%F A168783 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)/(36*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%t A168783 coxG[{19,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 09 2014 *)
%t A168783 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)/(36*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)
%Y A168783 Cf. A003952 (G.f.: (1+x)/(1-9*x)).
%K A168783 nonn,easy
%O A168783 0,2
%A A168783 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009