cp's OEIS Frontend

A170066 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170066 #6 Nov 26 2016 10:00:04
%S A170066 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170066 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170066 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170066 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170066 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170066 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170066 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A170066 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 A170066 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 A170066 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 A170066 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 A170066 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^37 - 7*t^36 - 7*t^35 -
%F A170066 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 -
%F A170066 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 -
%F A170066 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 -
%F A170066 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 -
%F A170066 7*t + 1)
%K A170066 nonn
%O A170066 0,2
%A A170066 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009