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A170455 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170455 #12 Nov 21 2016 16:48:53
%S A170455 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A170455 148462991222,1930018885886,25090245516518,326173191714734,
%U A170455 4240251492291542,55123269399790046,716602502197270598
%N A170455 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170455 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A170455 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170455 Vincenzo Librandi, <a href="/A170455/b170455.txt">Table of n, a(n) for n = 0..200</a>
%H A170455 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A170455 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 A170455 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 A170455 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 A170455 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 A170455 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 A170455 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(78*t^45 - 12*t^44 - 12*t^43 -
%F A170455 12*t^42 - 12*t^41 - 12*t^40 - 12*t^39 - 12*t^38 - 12*t^37 - 12*t^36 -
%F A170455 12*t^35 - 12*t^34 - 12*t^33 - 12*t^32 - 12*t^31 - 12*t^30 - 12*t^29 -
%F A170455 12*t^28 - 12*t^27 - 12*t^26 - 12*t^25 - 12*t^24 - 12*t^23 - 12*t^22 -
%F A170455 12*t^21 - 12*t^20 - 12*t^19 - 12*t^18 - 12*t^17 - 12*t^16 - 12*t^15 -
%F A170455 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 -
%F A170455 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1)
%t A170455 With[{num=Total[2t^Range[44]]+t^45+1,den=Total[-12 t^Range[44]]+78t^45+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Aug 05 2014 *)
%K A170455 nonn
%O A170455 0,2
%A A170455 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009