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A169407 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169407 #14 May 08 2018 00:52:40
%S A169407 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A169407 34867844010,313810596090,2824295364810,25418658283290,
%U A169407 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A169407 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169407 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A169407 First disagreement is at index 32, the difference is 45. - _Klaus Brockhaus_, Jun 27 2011
%C A169407 Computed with Magma using commands similar to those used to compute A154638.
%H A169407 <a href="/index/Rec#order_32">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, 8, -36).
%F A169407 G.f.: (t^32 + 2*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^32 - 8*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).
%F A169407 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-8*sum(k=1..31, x^k)+36*x^32).
%t A169407 coxG[{32,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 23 2016 *)
%Y A169407 Cf. A003952 (G.f.: (1+x)/(1-9*x) ).
%K A169407 nonn
%O A169407 0,2
%A A169407 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009