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A170270 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170270 #8 Feb 05 2017 13:08:50
%S A170270 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170270 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170270 86016000000000000,1720320000000000000,34406400000000000000
%N A170270 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170270 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170270 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170270 <a href="/index/Rec#order_41">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, -190).
%F A170270 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170270 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170270 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170270 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170270 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 +
%F A170270 1)/(190*t^41 - 19*t^40 - 19*t^39 - 19*t^38 - 19*t^37 - 19*t^36 - 19*t^35
%F A170270 - 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 -
%F A170270 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 -
%F A170270 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 -
%F A170270 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 -
%F A170270 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170270 coxG[{41,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 05 2017 *)
%K A170270 nonn
%O A170270 0,2
%A A170270 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009