cp's OEIS Frontend

A169361 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169361 #15 Dec 17 2021 13:20:08
%S A169361 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A169361 28295372292,311249095212,3423740047332,37661140520652,
%U A169361 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A169361 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169361 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A169361 First disagreement at index 31: a(31) = 209392827226636887822705645045546, A003954(31) = 209392827226636887822705645045612. - _Klaus Brockhaus_, Jun 17 2011
%C A169361 Computed with Magma using commands similar to those used to compute A154638.
%H A169361 <a href="/index/Rec#order_31">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, -55).
%F A169361 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*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^31 - 10*t^30 - 10*t^29 - 10*t^28 - 10*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 A169361 coxG[{31,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 17 2021 *)
%Y A169361 Cf. A003954 (G.f.: (1+x)/(1-11*x)).
%K A169361 nonn
%O A169361 0,2
%A A169361 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009