A169002 - OEIS

%I #10 Nov 25 2016 10:29:12

%S 1,37,1332,47952,1726272,62145792,2237248512,80540946432,

%T 2899474071552,104381066575872,3757718396731392,135277862282330112,

%U 4870003042163884032,175320109517899825152,6311523942644393705472

%N Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%C The initial terms coincide with those of A170756, although the two sequences are eventually different.

%C First disagreement at index 23: a(23) = 640998098126634736021008342268771686, A170756(23) = 640998098126634736021008342268772352. - Klaus Brockhaus, Apr 19 2011

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

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).

%F G.f.: (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)/(630*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).

%t With[{num=Total[2t^Range[22]]+t^23+1,den=Total[-35 t^Range[22]]+630t^23+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 18 2013 *)

%Y Cf. A170756 (G.f.: (1+x)/(1-36*x)).

%K nonn

%O 0,2

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