A169000 - OEIS

%I #10 Sep 03 2022 17:25:16

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

%T 1838317255040,62502786671360,2125094746826240,72253221392092160,

%U 2456609527331133440,83524723929258536960,2839840613594790256640,96554580862222868725760

%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)^23 = I.

%C The initial terms coincide with those of A170754, although the two sequences are eventually different.

%C First disagreement at index 23: a(23) = 172426581993545567312406146145320365, A170754(23) = 172426581993545567312406146145320960. - Klaus Brockhaus, Apr 19 2011

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

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

%F G.f.: (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)/(561*t^23 - 33*t^22 - 33*t^21 - 33*t^20 - 33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*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 coxG[{23,561,-33}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 03 2022 *)

%Y Cf. A170754 (G.f.: (1+x)/(1-34*x)).

%K nonn

%O 0,2

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