cp's OEIS Frontend

A170715 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170715 #24 Feb 12 2023 15:54:57
%S A170715 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A170715 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A170715 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A170715 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170715 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A170715 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170715 About the initial comment, first disagreement is at index 50 and the difference is 561.  - _Vincenzo Librandi_, Dec 06 2012
%H A170715 Vincenzo Librandi, <a href="/A170715/b170715.txt">Table of n, a(n) for n = 0..200</a>
%H A170715 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A170715 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
%F A170715 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170715 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170715 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170715 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170715 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 +
%F A170715 2*t + 1)/(528*t^50 - 32*t^49 - 32*t^48 - 32*t^47 - 32*t^46 - 32*t^45 -
%F A170715 32*t^44 - 32*t^43 - 32*t^42 - 32*t^41 - 32*t^40 - 32*t^39 - 32*t^38 -
%F A170715 32*t^37 - 32*t^36 - 32*t^35 - 32*t^34 - 32*t^33 - 32*t^32 - 32*t^31 -
%F A170715 32*t^30 - 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 -
%F A170715 32*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 -
%F A170715 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 -
%F A170715 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 -
%F A170715 32*t + 1).
%t A170715 With[{num = Total[2 t^Range[49]]+ t^50 + 1, den = Total[-32  t^Range[49]] + 528 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170715 coxG[{50,528,-32}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Feb 12 2023 *)
%K A170715 nonn
%O A170715 0,2
%A A170715 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009