A169448 - OEIS

%I #8 Nov 26 2016 07:11:08

%S 1,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49152,98304,

%T 196608,393216,786432,1572864,3145728,6291456,12582912,25165824,

%U 50331648,100663296,201326592,402653184,805306368,1610612736,3221225472

%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%C The initial terms coincide with those of A003945, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

%F G.f. (t^32 + t^31 + t^30 + t^29 + t^28 + t^27 + t^26 + t^25 + t^24 + t^23 + t^22

%F + t^21 + t^20 + t^19 + t^18 + t^17 + t^16 + t^15 + t^14 + t^13 + t^12 +

%F t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t +

%F 1)/(t^32 - 2*t^31 + t^30 - 2*t^29 + t^28 - 2*t^27 + t^26 - 2*t^25 + t^24

%F - 2*t^23 + t^22 - 2*t^21 + t^20 - 2*t^19 + t^18 - 2*t^17 + t^16 - 2*t^15

%F + t^14 - 2*t^13 + t^12 - 2*t^11 + t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 -

%F 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1)

%t With[{num=Total[t^Range[32]]+1,den=Total[-2 t^Range[1,31,2]] + Total[ t^Range[2,32,2]]+1},CoefficientList[Series[num/den,{t,0,40}],t]] (* _Harvey P. Dale_, Aug 10 2012 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009