cp's OEIS Frontend

A170458 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170458 #9 Nov 21 2016 16:50:34
%S A170458 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170458 73014444032,1168231104512,18691697672192,299067162755072,
%U A170458 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170458 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170458 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170458 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170458 <a href="/index/Rec#order_45">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, -120).
%F A170458 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170458 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170458 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 A170458 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 A170458 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 A170458 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^45 - 15*t^44 - 15*t^43 -
%F A170458 15*t^42 - 15*t^41 - 15*t^40 - 15*t^39 - 15*t^38 - 15*t^37 - 15*t^36 -
%F A170458 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 - 15*t^31 - 15*t^30 - 15*t^29 -
%F A170458 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 -
%F A170458 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 -
%F A170458 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 -
%F A170458 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1)
%t A170458 With[{num=Total[2t^Range[44]]+t^45+1,den=Total[-15 t^Range[44]]+ 120t^45+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 23 2012 *)
%K A170458 nonn
%O A170458 0,2
%A A170458 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009