%I #12 Nov 24 2016 10:45:12
%S 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T 67077144576,804925734912,9659108818944,115909305827328,
%U 1390911669927858,16690940039133360,200291280469589166
%N Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
%C The initial terms coincide with those of A170732, 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="/A167114/b167114.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
%F G.f.: (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)/(66*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
%t coxG[{14,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 25 2016 *)
%t CoefficientList[Series[(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)/ (66*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 03 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009