A169434 - OEIS

%I #13 May 08 2018 01:05:32

%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)^32 = I.

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

%C First disagreement is at index 32, the difference is 666. - _Klaus Brockhaus_, Jun 30 2011

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

%H <a href="/index/Rec#order_32">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, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).

%F G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*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)/(630*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*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).

%F G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-35*sum(k=1..31,x^k)+630*x^32).

%t With[{num=Total[2t^Range[31]]+t^32+1,den=Total[-35 t^Range[31]]+ 630t^32+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 03 2012 *)

%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