cp's OEIS Frontend

A170026 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170026 #9 Nov 26 2016 09:41:50
%S A170026 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170026 73014444032,1168231104512,18691697672192,299067162755072,
%U A170026 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170026 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170026 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170026 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170026 <a href="/index/Rec#order_36">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, -120).
%F A170026 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170026 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 A170026 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 A170026 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 A170026 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^36 - 15*t^35 - 15*t^34 - 15*t^33 -
%F A170026 15*t^32 - 15*t^31 - 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 -
%F A170026 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 -
%F A170026 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 -
%F A170026 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4
%F A170026 - 15*t^3 - 15*t^2 - 15*t + 1)
%t A170026 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-15 t^Range[35]]+ 120t^36+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Nov 12 2011 *)
%K A170026 nonn
%O A170026 0,2
%A A170026 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009