A169432 - OEIS

%I #13 May 08 2018 01:02:32

%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)^32 = I.

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

%C First disagreement is at index 32, the difference is 595. - _Klaus Brockhaus_, Jun 30 2011

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

%H <a href="/index/Rec#order_32">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, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

%F G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*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^32 - 33*t^31 - 33*t^30 - 33*t^29 - 33*t^28 - 33*t^27 - 33*t^26 - 33*t^25 - 33*t^24 - 33*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).

%F G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-33*sum(k=1..31,x^k)+561*x^32).

%t coxG[{32,561,-33}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 10 2017 *)

%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