cp's OEIS Frontend

A170664 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170664 #8 Nov 21 2016 11:27:51
%S A170664 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170664 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170664 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170664 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170664 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170664 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170664 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A170664 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170664 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170664 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 A170664 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 A170664 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 A170664 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 A170664 1)/(435*t^49 - 29*t^48 - 29*t^47 - 29*t^46 - 29*t^45 - 29*t^44 - 29*t^43
%F A170664 - 29*t^42 - 29*t^41 - 29*t^40 - 29*t^39 - 29*t^38 - 29*t^37 - 29*t^36 -
%F A170664 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 -
%F A170664 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 -
%F A170664 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 -
%F A170664 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 -
%F A170664 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170664 With[{num=Total[2t^Range[48]]+t^49+1,den=Total[-29 t^Range[48]]+435t^49+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Apr 01 2013 *)
%K A170664 nonn
%O A170664 0,2
%A A170664 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009