cp's OEIS Frontend

A169310 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169310 #10 May 10 2018 01:37:44
%S A169310 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A169310 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A169310 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A169310 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169310 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A169310 First disagreement at index 30: a(30) = 1392682544196052809261514716, A003951(30) = 1392682544196052809261514752. - _Klaus Brockhaus_, Jun 22 2011
%C A169310 Computed with Magma using commands similar to those used to compute A154638.
%H A169310 <a href="/index/Rec#order_30">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, -28).
%F A169310 G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 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 - 7*t + 1).
%Y A169310 Cf. A003951 (G.f.: (1+x)/(1-8*x)).
%K A169310 nonn
%O A169310 0,2
%A A169310 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009