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A170398 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170398 #9 Nov 21 2016 17:16:34
%S A170398 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170398 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170398 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170398 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170398 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170398 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170398 <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A170398 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170398 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170398 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170398 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170398 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170398 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^44 - 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40 -
%F A170398 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 - 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 -
%F A170398 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 -
%F A170398 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 -
%F A170398 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 -
%F A170398 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1)
%t A170398 With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-3 t^Range[43]]+ 6t^44+1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 19 2012 *)
%K A170398 nonn
%O A170398 0,2
%A A170398 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009