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A169359 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169359 #14 May 08 2018 01:13:35
%S A169359 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A169359 34867844010,313810596090,2824295364810,25418658283290,
%U A169359 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A169359 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169359 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A169359 First disagreement at index 31: a(31) = 423911582752162035142944331965, A003952(31) = 423911582752162035142944332010. - _Klaus Brockhaus_, Jun 17 2011
%C A169359 Computed with Magma using commands similar to those used to compute A154638.
%H A169359 <a href="/index/Rec#order_31">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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).
%F A169359 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*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^31 - 8*t^30 - 8*t^29 - 8*t^28 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22 - 8*t^21 - 8*t^20 - 8*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 A169359 coxG[{31,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 13 2015 *)
%Y A169359 Cf. A003952 (G.f.: (1+x)/(1-9*x)).
%K A169359 nonn
%O A169359 0,2
%A A169359 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009