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A169370 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169370 #13 May 08 2018 00:32:18
%S A169370 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A169370 537600000000,10752000000000,215040000000000,4300800000000000,
%U A169370 86016000000000000,1720320000000000000,34406400000000000000
%N A169370 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169370 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A169370 First disagreement at index 31: a(31) = 22548578303999999999999999999999999999790, A170740(31) = 22548578304000000000000000000000000000000. - _Klaus Brockhaus_, Jun 17 2011
%C A169370 Computed with Magma using commands similar to those used to compute A154638.
%H A169370 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A169370 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)/(190*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%t A169370 coxG[{31,190,-19}] (* coxG program taken from A169452 *) (* _Harvey P. Dale_, Aug 16 2014 *)
%Y A169370 Cf. A170740 (G.f.: (1+x)/(1-20*x)).
%K A169370 nonn
%O A169370 0,2
%A A169370 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009