A168910 - OEIS

%I #10 Nov 25 2016 09:43:05

%S 1,41,1640,65600,2624000,104960000,4198400000,167936000000,

%T 6717440000000,268697600000000,10747904000000000,429916160000000000,

%U 17196646400000000000,687865856000000000000,27514634240000000000000

%N Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

%C The initial terms coincide with those of A170760, although the two sequences are eventually different.

%C First disagreement at index 21: a(21) = 4507997673881599999999999999999180, A170760(21) = 4507997673881600000000000000000000. - Klaus Brockhaus, Apr 05 2011

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

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

%F G.f.: (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)/(780*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

%t With[{num=Total[2t^Range[20]]+t^21+1,den=Total[-39 t^Range[20]]+ 780t^21+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 05 2012 *)

%Y Cf. A170760 (G.f.: (1+x)/(1-40*x)).

%K nonn

%O 0,2

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