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A170376 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170376 #10 Sep 29 2024 11:42:07
%S A170376 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170376 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170376 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170376 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170376 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170376 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170376 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A170376 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170376 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170376 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170376 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170376 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
%F A170376 + 2*t^2 + 2*t + 1)/(435*t^43 - 29*t^42 - 29*t^41 - 29*t^40 - 29*t^39 -
%F A170376 29*t^38 - 29*t^37 - 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 -
%F A170376 29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 -
%F A170376 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 -
%F A170376 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 -
%F A170376 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 -
%F A170376 29*t^2 - 29*t + 1)
%t A170376 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-29 t^Range[42]]+435t^43+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 26 2013 *)
%t A170376 coxG[{43,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 29 2024 *)
%K A170376 nonn
%O A170376 0,2
%A A170376 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009