A167088 - OEIS

%I #10 Nov 24 2016 10:33:22

%S 1,35,1190,40460,1375640,46771760,1590239840,54068154560,

%T 1838317255040,62502786671360,2125094746826240,72253221392092160,

%U 2456609527331133440,83524723929258536365,2839840613594790216180,96554580862222866662895

%N Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

%C The initial terms coincide with those of A170754, 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="/A167088/b167088.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

%F G.f.: (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)/(561*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

%t CoefficientList[Series[(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)/(561*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 01 2016 *)

%K nonn

%O 0,2

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