A169169 - OEIS

%I #10 Mar 07 2020 15:03:55

%S 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,

%T 28295372292,311249095212,3423740047332,37661140520652,

%U 414272545727172,4556998002998892,50126978032987812,551396758362865932

%N Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%C The initial terms coincide with those of A003954, although the two sequences are eventually different.

%C First disagreement at index 27: a(27) = 14301811845272651309521593066, A003954(27) = 14301811845272651309521593132. - Klaus Brockhaus, May 07 2011

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

%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).

%F G.f.: (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)/(55*t^27 - 10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

%t coxG[{27,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 07 2020 *)

%Y Cf. A003954 (G.f.: (1+x)/(1-11*x)).

%K nonn

%O 0,2

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