cp's OEIS Frontend

A169505 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169505 #8 Sep 05 2020 15:47:38
%S A169505 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A169505 28295372292,311249095212,3423740047332,37661140520652,
%U A169505 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A169505 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169505 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A169505 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169505 <a href="/index/Rec#order_34">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, 10, 10, 10, 10, 10, 10, 10, -55).
%F A169505 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169505 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169505 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169505 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 +
%F A169505 2*t + 1)/(55*t^34 - 10*t^33 - 10*t^32 - 10*t^31 - 10*t^30 - 10*t^29 -
%F A169505 10*t^28 - 10*t^27 - 10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 -
%F A169505 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 -
%F A169505 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 -
%F A169505 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1)
%t A169505 coxG[{34,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 05 2020 *)
%K A169505 nonn
%O A169505 0,2
%A A169505 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009