cp's OEIS Frontend

A169274 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169274 #12 May 10 2018 02:02:37
%S A169274 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A169274 537600000000,10752000000000,215040000000000,4300800000000000,
%U A169274 86016000000000000,1720320000000000000,34406400000000000000
%N A169274 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169274 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A169274 First disagreement at index 29: a(29) = 56371445759999999999999999999999999790, A170740(29) = 56371445760000000000000000000000000000. - _Klaus Brockhaus_, Jun 03 2011
%C A169274 Computed with Magma using commands similar to those used to compute A154638.
%H A169274 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A169274 G.f.: (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)/(190*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%t A169274 With[{num=Total[2t^Range[28]]+t^29+1,den=Total[-19 t^Range[28]]+ 190t^29+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 19 2012 *)
%Y A169274 Cf. A170740 (G.f.: (1+x)/(1-20*x)).
%K A169274 nonn
%O A169274 0,2
%A A169274 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009