cp's OEIS Frontend

A170627 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170627 #8 Nov 21 2016 12:21:44
%S A170627 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170627 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170627 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170627 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170627 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170627 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170627 <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170627 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170627 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170627 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 A170627 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 A170627 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 A170627 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170627 1)/(820*t^48 - 40*t^47 - 40*t^46 - 40*t^45 - 40*t^44 - 40*t^43 - 40*t^42
%F A170627 - 40*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35 -
%F A170627 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 -
%F A170627 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 -
%F A170627 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 -
%F A170627 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 -
%F A170627 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%t A170627 With[{num=Total[2t^Range[47]]+t^48+1,den=Total[-40 t^Range[47]]+820t^48+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 14 2014 *)
%K A170627 nonn
%O A170627 0,2
%A A170627 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009