cp's OEIS Frontend

A170314 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170314 #6 Nov 22 2016 08:09:15
%S A170314 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170314 73014444032,1168231104512,18691697672192,299067162755072,
%U A170314 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170314 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170314 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170314 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170314 <a href="/index/Rec#order_42">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, -120).
%F A170314 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170314 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 A170314 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 A170314 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 A170314 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 A170314 2*t + 1)/(120*t^42 - 15*t^41 - 15*t^40 - 15*t^39 - 15*t^38 - 15*t^37 -
%F A170314 15*t^36 - 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 - 15*t^31 - 15*t^30 -
%F A170314 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 -
%F A170314 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 -
%F A170314 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 -
%F A170314 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1)
%K A170314 nonn
%O A170314 0,2
%A A170314 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009