A168846 - OEIS

%I #11 Nov 24 2016 18:35:54

%S 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,

%T 2751882854400,66045188505600,1585084524134400,38042028579225600,

%U 913008685901414400,21912208461633945600,525893003079214694400

%N Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%C The initial terms coincide with those of A170744, although the two sequences are eventually different.

%C First disagreement at index 20: a(20) = 4187488247750628826782105300, A170744(20) = 4187488247750628826782105600. - Klaus Brockhaus, Apr 02 2011

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

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

%F G.f.: (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)/(276*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

%t With[{num=Total[2t^Range[19]]+t^20+1,den=Total[-23 t^Range[19]]+ 276t^20+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 20 2011 *)

%Y Cf. A170744 (G.f.: (1+x)/(1-24*x)).

%K nonn

%O 0,2

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