A168690 - OEIS

%I #14 Nov 24 2016 13:02:31

%S 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,

%T 67077144576,804925734912,9659108818944,115909305827328,

%U 1390911669927936,16690940039135232,200291280469622784

%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)^17 = I.

%C The initial terms coincide with those of A170732, although the two sequences are eventually different.

%C First disagreement at index 17: a(17) = 2403495365635473330, A170732(17) = 2403495365635473408. - _Klaus Brockhaus_, Mar 30 2011

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

%H G. C. Greubel, <a href="/A168690/b168690.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

%F G.f.: (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)/ (66*t^17 - 11*t^16 - 11*t^15 - 11*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 CoefficientList[Series[(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)/(66*t^17 - 11*t^16 - 11*t^15 - 11*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_, Aug 03 2016 *)

%Y Cf. A170732 (G.f.: (1+x)/(1-12*x)).

%K nonn

%O 0,2

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