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A170318 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170318 #8 Nov 22 2016 08:11:33
%S A170318 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170318 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170318 86016000000000000,1720320000000000000,34406400000000000000
%N A170318 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170318 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170318 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170318 <a href="/index/Rec#order_42">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, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170318 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 A170318 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 A170318 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 A170318 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 A170318 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 A170318 2*t + 1)/(190*t^42 - 19*t^41 - 19*t^40 - 19*t^39 - 19*t^38 - 19*t^37 -
%F A170318 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 -
%F A170318 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 -
%F A170318 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 -
%F A170318 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 -
%F A170318 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 A170318 coxG[{42,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 24 2014 *)
%K A170318 nonn
%O A170318 0,2
%A A170318 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009