A169255 - OEIS

%I #18 Dec 15 2024 11:47:02

%S 1,50,2450,120050,5882450,288240050,14123762450,692064360050,

%T 33911153642450,1661646528480050,81420679895522450,

%U 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450

%N Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%C The initial terms coincide with those of A170769, although the two sequences are eventually different.

%C First disagreement at index 28: a(28) = 215905728369821828201764654885386404377612441225, A170769(28) = 215905728369821828201764654885386404377612442450. - _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 (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).

%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)/(1176*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).

%t With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-48 t^Range[27]]+ 1176t^28+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 23 2011 *)

%t coxG[{28,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 15 2024 *)

%Y Cf. A170769 (G.f.: (1+x)/(1-49*x)).

%K nonn

%O 0,2

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