cp's OEIS Frontend

A170698 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170698 #12 Nov 21 2016 10:45:06
%S A170698 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170698 73014444032,1168231104512,18691697672192,299067162755072,
%U A170698 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170698 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170698 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170698 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170698 About the initial comment, first disagreement is at index 50 and the difference is 136.  - _Vincenzo Librandi_, Dec 08 2012
%H A170698 Vincenzo Librandi, <a href="/A170698/b170698.txt">Table of n, a(n) for n = 0..200</a>
%H A170698 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).
%F A170698 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 A170698 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 A170698 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 A170698 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 A170698 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 A170698 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 A170698 2*t + 1)/(120*t^50 - 15*t^49 - 15*t^48 - 15*t^47 - 15*t^46 - 15*t^45 -
%F A170698 15*t^44 - 15*t^43 - 15*t^42 - 15*t^41 - 15*t^40 - 15*t^39 - 15*t^38 -
%F A170698 15*t^37 - 15*t^36 - 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 - 15*t^31 -
%F A170698 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 -
%F A170698 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 -
%F A170698 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 -
%F A170698 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 -
%F A170698 15*t + 1).
%t A170698 With[{num=Total[2 t^Range[49]] + t^50 + 1, den=Total[-15 t^Range[49]] + 120 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}],t]] (* _Harvey P. Dale_, Dec 02 2012 *)
%K A170698 nonn
%O A170698 0,2
%A A170698 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009