cp's OEIS Frontend

A170224 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170224 #9 Nov 22 2016 15:21:33
%S A170224 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170224 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170224 295665060514131968,6504631331310903296,143101889288839872512
%N A170224 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170224 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170224 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170224 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231)
%F A170224 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170224 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170224 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170224 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170224 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170224 1)/(231*t^40 - 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 - 21*t^35 - 21*t^34
%F A170224 - 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 -
%F A170224 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 -
%F A170224 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 -
%F A170224 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5
%F A170224 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170224 With[{num=Total[2t^Range[39]]+t^40+1,den=Total[-21 t^Range[39]]+ 231t^40+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 17 2012 *)
%K A170224 nonn
%O A170224 0,2
%A A170224 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009