%I #14 Oct 22 2022 09:28:16

%S 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,

%T 34867844010,313810596090,2824295364810,25418658283290,

%U 228767924549610,2058911320946490,18530201888518410,166771816996665645

%N Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%C The initial terms coincide with those of A003952, although the two sequences are eventually different.

%C First disagreement at index 18: a(18) = 166771816996665645, A003952(18) = 166771816996665690. - _Klaus Brockhaus_, Mar 27 2011

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A168735/b168735.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_18">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, -36).

%F G.f.: (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^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 CoefficientList[Series[(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^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 08 2016 *)

%t coxG[{18,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 22 2022 *)

%Y Cf. A003952 (G.f.: (1+x)/(1-9*x)).

%K nonn,easy

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009