A167674 - OEIS

%I #9 Nov 24 2016 11:05:07

%S 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,

%T 125563633938,2134581776946,36287890208082,616894133537394,

%U 10487200270135698,178282404592306866,3030800878069216569,51523614927176679072

%N Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%C The initial terms coincide with those of A170737, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A167674/b167674.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).

%F G.f.: (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)/(136*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

%t CoefficientList[Series[(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)/(136*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 19 2016 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009