A169418 - OEIS

%I #14 Jun 05 2019 10:42:14

%S 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,

%T 537600000000,10752000000000,215040000000000,4300800000000000,

%U 86016000000000000,1720320000000000000,34406400000000000000

%N Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%C The initial terms coincide with those of A170740, although the two sequences are eventually different.

%C First disagreement is at index 32, the difference is 210. - _Klaus Brockhaus_, Jun 27 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

%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)/(190*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

%F G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-19*sum(k=1..31, x^k)+190*x^32).

%t coxG[{32,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 05 2019 *)

%Y Cf. A170740 (G.f.: (1+x)/(1-20*x) ).

%K nonn

%O 0,2

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