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A170328 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170328 #8 Nov 22 2016 08:18:09
%S A170328 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170328 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170328 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170328 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170328 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170328 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170328 <a href="/index/Rec#order_42">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, -435).
%F A170328 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170328 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170328 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170328 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170328 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 +
%F A170328 2*t + 1)/(435*t^42 - 29*t^41 - 29*t^40 - 29*t^39 - 29*t^38 - 29*t^37 -
%F A170328 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 -
%F A170328 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 -
%F A170328 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 -
%F A170328 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 -
%F A170328 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170328 coxG[{42,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 04 2015 *)
%K A170328 nonn
%O A170328 0,2
%A A170328 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009