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A170482 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170482 #8 Nov 21 2016 17:05:07
%S A170482 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A170482 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A170482 17196646400000000000,687865856000000000000,27514634240000000000000
%N A170482 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170482 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A170482 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170482 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A170482 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170482 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170482 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170482 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170482 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170482 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^45 - 39*t^44 - 39*t^43 -
%F A170482 39*t^42 - 39*t^41 - 39*t^40 - 39*t^39 - 39*t^38 - 39*t^37 - 39*t^36 -
%F A170482 39*t^35 - 39*t^34 - 39*t^33 - 39*t^32 - 39*t^31 - 39*t^30 - 39*t^29 -
%F A170482 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 -
%F A170482 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 -
%F A170482 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 -
%F A170482 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1)
%t A170482 coxG[{45,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 27 2015 *)
%K A170482 nonn
%O A170482 0,2
%A A170482 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009