cp's OEIS Frontend

A170556 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170556 #9 Nov 21 2016 12:52:58
%S A170556 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170556 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170556 21979796247097344,395636332447752192,7121453984059539456
%N A170556 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170556 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170556 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170556 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).
%F A170556 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170556 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170556 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170556 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170556 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170556 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^47 -
%F A170556 17*t^46 - 17*t^45 - 17*t^44 - 17*t^43 - 17*t^42 - 17*t^41 - 17*t^40 -
%F A170556 17*t^39 - 17*t^38 - 17*t^37 - 17*t^36 - 17*t^35 - 17*t^34 - 17*t^33 -
%F A170556 17*t^32 - 17*t^31 - 17*t^30 - 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 -
%F A170556 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 -
%F A170556 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 -
%F A170556 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4
%F A170556 - 17*t^3 - 17*t^2 - 17*t + 1)
%t A170556 With[{num=Total[2t^Range[46]]+t^47+1,den=Total[-17 t^Range[46]]+ 153t^47+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 01 2012 *)
%K A170556 nonn
%O A170556 0,2
%A A170556 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009