cp's OEIS Frontend

A170609 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170609 #8 Nov 21 2016 12:11:10
%S A170609 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170609 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170609 525950986368487704,12096872686475217192,278228071788929995416
%N A170609 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170609 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170609 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170609 <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A170609 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 A170609 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 A170609 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 A170609 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 A170609 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 A170609 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170609 1)/(253*t^48 - 22*t^47 - 22*t^46 - 22*t^45 - 22*t^44 - 22*t^43 - 22*t^42
%F A170609 - 22*t^41 - 22*t^40 - 22*t^39 - 22*t^38 - 22*t^37 - 22*t^36 - 22*t^35 -
%F A170609 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 - 22*t^30 - 22*t^29 - 22*t^28 -
%F A170609 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 -
%F A170609 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 -
%F A170609 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 -
%F A170609 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)
%t A170609 With[{num=Total[2t^Range[47]]+t^48+1,den=Total[-22 t^Range[47]]+ 253t^48+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 12 2012 *)
%K A170609 nonn
%O A170609 0,2
%A A170609 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009