cp's OEIS Frontend

A170117 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170117 #8 Mar 11 2023 10:01:32
%S A170117 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A170117 28295372292,311249095212,3423740047332,37661140520652,
%U A170117 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A170117 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170117 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A170117 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170117 <a href="/index/Rec#order_38">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, -55).
%F A170117 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170117 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170117 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170117 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170117 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^38 - 10*t^37 -
%F A170117 10*t^36 - 10*t^35 - 10*t^34 - 10*t^33 - 10*t^32 - 10*t^31 - 10*t^30 -
%F A170117 10*t^29 - 10*t^28 - 10*t^27 - 10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 -
%F A170117 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 -
%F A170117 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 -
%F A170117 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 A170117 coxG[{38,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 11 2023 *)
%K A170117 nonn
%O A170117 0,2
%A A170117 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009