cp's OEIS Frontend

A169093 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169093 #10 Nov 25 2016 12:01:30
%S A169093 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A169093 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A169093 25205209081233592352,781361481518241362912,24222205927065482250272
%N A169093 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169093 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A169093 First disagreement at index 25: a(25) = 19853205150896886022025614450341027376, A170751(25) = 19853205150896886022025614450341027872. - Klaus Brockhaus, Apr 25 2011
%C A169093 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169093 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A169093 G.f.: (t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%t A169093 With[{num=Total[2t^Range[24]]+t^25+1,den=Total[-30 t^Range[24]]+465t^25+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 20 2012 *)
%Y A169093 Cf. A170751 (G.f.: (1+x)/(1-31*x)).
%K A169093 nonn
%O A169093 0,2
%A A169093 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009