cp's OEIS Frontend

A170412 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170412 #8 Sep 03 2018 11:39:16
%S A170412 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170412 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170412 21979796247097344,395636332447752192,7121453984059539456
%N A170412 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170412 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170412 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170412 <a href="/index/Rec#order_44">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, -153).
%F A170412 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 A170412 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 A170412 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 A170412 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 A170412 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 A170412 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^44 - 17*t^43 - 17*t^42 - 17*t^41 -
%F A170412 17*t^40 - 17*t^39 - 17*t^38 - 17*t^37 - 17*t^36 - 17*t^35 - 17*t^34 -
%F A170412 17*t^33 - 17*t^32 - 17*t^31 - 17*t^30 - 17*t^29 - 17*t^28 - 17*t^27 -
%F A170412 17*t^26 - 17*t^25 - 17*t^24 - 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 -
%F A170412 17*t^19 - 17*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 -
%F A170412 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5
%F A170412 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1)
%t A170412 coxG[{44,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 03 2018 *)
%K A170412 nonn
%O A170412 0,2
%A A170412 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009