cp's OEIS Frontend

A169383 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169383 #15 Oct 11 2024 06:58:00
%S A169383 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A169383 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A169383 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A169383 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169383 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A169383 First disagreement at index 31: a(31) = 122151024375542614757685533510827119913667368305, A170753(31) = 122151024375542614757685533510827119913667368866. - _Klaus Brockhaus_, Jun 17 2011
%C A169383 Computed with Magma using commands similar to those used to compute A154638.
%H A169383 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A169383 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*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)/(528*t^31 - 32*t^30 - 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%t A169383 With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-32 t^Range[30]]+ 528t^31+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 04 2012 *)
%Y A169383 Cf. A170753 (G.f.: (1+x)/(1-33*x)).
%K A169383 nonn
%O A169383 0,2
%A A169383 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009