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A170462 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170462 #9 Nov 21 2016 16:52:58
%S A170462 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170462 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170462 86016000000000000,1720320000000000000,34406400000000000000
%N A170462 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170462 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170462 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170462 <a href="/index/Rec#order_45">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, 19, 19, 19, -190).
%F A170462 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 A170462 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 A170462 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 A170462 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 A170462 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 A170462 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^45 - 19*t^44 - 19*t^43 -
%F A170462 19*t^42 - 19*t^41 - 19*t^40 - 19*t^39 - 19*t^38 - 19*t^37 - 19*t^36 -
%F A170462 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 -
%F A170462 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 -
%F A170462 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 -
%F A170462 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 -
%F A170462 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170462 With[{num=Total[2t^Range[44]]+t^45+1, den=Total[-19 t^Range[44]]+ 190t^45+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 16 2011 *)
%K A170462 nonn
%O A170462 0,2
%A A170462 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009