cp's OEIS Frontend

A170414 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170414 #12 Nov 21 2016 17:25:30
%S A170414 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170414 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170414 86016000000000000,1720320000000000000,34406400000000000000
%N A170414 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170414 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170414 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170414 Vincenzo Librandi, <a href="/A170414/b170414.txt">Table of n, a(n) for n = 0..200</a>
%H A170414 <a href="/index/Rec#order_44">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, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170414 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170414 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170414 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170414 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170414 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
%F A170414 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^44 - 19*t^43 - 19*t^42 - 19*t^41 -
%F A170414 19*t^40 - 19*t^39 - 19*t^38 - 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 -
%F A170414 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 -
%F A170414 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 -
%F A170414 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 -
%F A170414 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5
%F A170414 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170414 With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-19 t^Range[43]]+190t^44+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 20 2014 *)
%K A170414 nonn
%O A170414 0,2
%A A170414 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009