cp's OEIS Frontend

A169073 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%I A169073 #10 Jul 03 2021 13:36:36
%S A169073 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A169073 28295372292,311249095212,3423740047332,37661140520652,
%U A169073 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A169073 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
%C A169073 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A169073 First disagreement at index 25: a(25) = 118196792109691333136542026, A003954(25) = 118196792109691333136542092. - Klaus Brockhaus, Apr 25 2011
%C A169073 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169073 <a href="/index/Rec#order_25">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, -55).
%F A169073 G.f.: (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^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 A169073 coxG[{25,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 03 2021 *)
%Y A169073 Cf. A003954 (G.f.: (1+x)/(1-11*x)).
%K A169073 nonn
%O A169073 0,2
%A A169073 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009