A169276 - OEIS

%I #14 May 10 2018 02:03:27

%S 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,

%T 1262145091328,27767192009216,610878224202752,13439320932460544,

%U 295665060514131968,6504631331310903296,143101889288839872512

%N Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%C The initial terms coincide with those of A170742, although the two sequences are eventually different.

%C First disagreement at index 29: a(29) = 890354379045016688408748795162974486275, A170742(29) = 890354379045016688408748795162974486528. - _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 (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

%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)/(231*t^29 - 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

%t With[{num=Total[2t^Range[28]]+t^29+1,den=Total[-21 t^Range[28]]+ 231t^29+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 25 2011 *)

%Y Cf. A170742 (G.f.: (1+x)/(1-22*x)).

%K nonn

%O 0,2

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