cp's OEIS Frontend

A170136 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170136 #16 Dec 10 2024 08:58:38
%S A170136 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170136 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170136 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170136 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170136 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170136 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170136 Vincenzo Librandi, <a href="/A170136/b170136.txt">Table of n, a(n) for n = 0..200</a>
%H A170136 <a href="/index/Rec#order_38">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, -435).
%F A170136 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170136 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170136 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170136 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170136 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^38 - 29*t^37 -
%F A170136 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 -
%F A170136 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 -
%F A170136 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 -
%F A170136 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 -
%F A170136 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170136 With[{num=Total[2t^Range[37]]+t^38+1,den=Total[-29 t^Range[37]]+ 435t^38+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 16 2012 *)
%K A170136 nonn
%O A170136 0,2
%A A170136 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009