A169208 - OEIS

%I #15 May 10 2018 02:17:48

%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 50331648,100663296,201326592,402653181,805306356,1610612703,3221225388

%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)^28 = I.

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

%C First disagreement at index 28: a(28) = 402653181, A003945(28) = 402653184. - _Klaus Brockhaus_, May 24 2011

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

%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).

%F G.f.: (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)/(t^28 - t^27 - t^26 - t^25 - t^24 - t^23 - t^22 - t^21 - t^20 - t^19 - t^18 - t^17 - t^16 - t^15 - t^14 - t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).

%t With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-t^Range[27]]+t^28+1}, CoefficientList[ Series[num/den,{t,0,35}],t]] (* _Harvey P. Dale_, Sep 09 2011 *)

%Y Cf. A003945 (G.f.: (1+x)/(1-2*x)).

%K nonn

%O 0,2

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