cp's OEIS Frontend

A170074 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170074 #11 Nov 26 2016 10:02:12
%S A170074 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170074 73014444032,1168231104512,18691697672192,299067162755072,
%U A170074 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170074 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170074 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170074 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170074 Vincenzo Librandi, <a href="/A170074/b170074.txt">Table of n, a(n) for n = 0..800</a>
%H A170074 <a href="/index/Rec#order_37">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, -120).
%F A170074 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170074 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170074 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170074 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170074 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^37 - 15*t^36 - 15*t^35 -
%F A170074 15*t^34 - 15*t^33 - 15*t^32 - 15*t^31 - 15*t^30 - 15*t^29 - 15*t^28 -
%F A170074 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 -
%F A170074 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 -
%F A170074 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 -
%F A170074 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1)
%t A170074 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-15 t^Range[36]]+120t^37+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 03 2013 *)
%K A170074 nonn
%O A170074 0,2
%A A170074 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009