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A170272 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170272 #8 Nov 22 2016 11:49:11
%S A170272 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170272 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170272 295665060514131968,6504631331310903296,143101889288839872512
%N A170272 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170272 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170272 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170272 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170272 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 A170272 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 A170272 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 A170272 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 A170272 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 A170272 1)/(231*t^41 - 21*t^40 - 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 - 21*t^35
%F A170272 - 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 -
%F A170272 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 -
%F A170272 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 -
%F A170272 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 -
%F A170272 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170272 coxG[{41,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 16 2014 *)
%K A170272 nonn
%O A170272 0,2
%A A170272 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009