cp's OEIS Frontend

A170165 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170165 #10 Jan 30 2023 19:02:41
%S A170165 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A170165 28295372292,311249095212,3423740047332,37661140520652,
%U A170165 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A170165 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170165 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A170165 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170165 <a href="/index/Rec#order_39">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, 10, 10, 10, 10, 10, -55).
%F A170165 G.f.: (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170165 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170165 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170165 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170165 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^39 -
%F A170165 10*t^38 - 10*t^37 - 10*t^36 - 10*t^35 - 10*t^34 - 10*t^33 - 10*t^32 -
%F A170165 10*t^31 - 10*t^30 - 10*t^29 - 10*t^28 - 10*t^27 - 10*t^26 - 10*t^25 -
%F A170165 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 -
%F A170165 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 -
%F A170165 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 -
%F A170165 10*t^2 - 10*t + 1).
%t A170165 coxG[{39,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 30 2023 *)
%K A170165 nonn
%O A170165 0,2
%A A170165 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009