A169257 - OEIS

%I #13 May 10 2018 01:54:42

%S 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764,

%T 6377292,19131876,57395628,172186884,516560652,1549681956,4649045868,

%U 13947137604,41841412812,125524238436,376572715308,1129718145924

%N Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%C The initial terms coincide with those of A003946, although the two sequences are eventually different.

%C First disagreement at index 29: a(29) = 91507169819838, A003946(29) = 91507169819844. - _Klaus Brockhaus_, Jun 03 2011

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

%H <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

%F G.f.: (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)/(3*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).

%t With[{num=Total[2t^Range[28]]+t^29+1,den=Total[-2 t^Range[28]]+3t^29+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 26 2012 *)

%Y Cf. A003946 (G.f.: (1+x)/(1-3*x)).

%K nonn

%O 0,2

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