cp's OEIS Frontend

A170718 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170718 #16 Aug 06 2019 11:37:52
%S A170718 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A170718 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A170718 4870003042163884032,175320109517899825152,6311523942644393705472
%N A170718 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170718 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A170718 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170718 About the initial comment, first disagreement is at index 50 and the difference is 666.  - _Vincenzo Librandi_, Dec 06 2012
%H A170718 Vincenzo Librandi, <a href="/A170718/b170718.txt">Table of n, a(n) for n = 0..200</a>
%H A170718 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A170718 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 A170718 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 A170718 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 A170718 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 A170718 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 A170718 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 A170718 2*t + 1)/(630*t^50 - 35*t^49 - 35*t^48 - 35*t^47 - 35*t^46 - 35*t^45 -
%F A170718 35*t^44 - 35*t^43 - 35*t^42 - 35*t^41 - 35*t^40 - 35*t^39 - 35*t^38 -
%F A170718 35*t^37 - 35*t^36 - 35*t^35 - 35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 -
%F A170718 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 -
%F A170718 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 -
%F A170718 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 -
%F A170718 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 -
%F A170718 35*t + 1)
%t A170718 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-35  t^Range[49]] + 630 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 201}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170718 coxG[{42,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 06 2019 *)
%K A170718 nonn
%O A170718 0,2
%A A170718 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009