cp's OEIS Frontend

A170018 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170018 #6 Nov 26 2016 09:39:28
%S A170018 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170018 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170018 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170018 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170018 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170018 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170018 <a href="/index/Rec#order_36">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, -28).
%F A170018 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 A170018 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 A170018 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 A170018 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 A170018 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^36 - 7*t^35 - 7*t^34 - 7*t^33 - 7*t^32
%F A170018 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24
%F A170018 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16
%F A170018 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 -
%F A170018 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1)
%K A170018 nonn
%O A170018 0,2
%A A170018 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009