A169120 - OEIS

%I #10 Apr 29 2019 09:27:54

%S 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,

%T 11000000000,110000000000,1100000000000,11000000000000,

%U 110000000000000,1100000000000000,11000000000000000,110000000000000000

%N Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%C The initial terms coincide with those of A003953, although the two sequences are eventually different.

%C First disagreement at index 26: a(26) = 109999999999999999999999945, A003953(26) = 110000000000000000000000000. - Klaus Brockhaus, Apr 30 2011

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

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

%F G.f.: (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)/(45*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

%t coxG[{26,45,-9}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 29 2019 *)

%Y Cf. A003953 (G.f.: (1+x)/(1-10*x)).

%K nonn

%O 0,2

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