cp's OEIS Frontend

A170021 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170021 #8 Nov 26 2016 09:40:24
%S A170021 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A170021 28295372292,311249095212,3423740047332,37661140520652,
%U A170021 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A170021 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170021 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A170021 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170021 <a href="/index/Rec#order_36">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, -55).
%F A170021 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170021 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170021 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170021 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
%F A170021 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^36 - 10*t^35 - 10*t^34 - 10*t^33 -
%F A170021 10*t^32 - 10*t^31 - 10*t^30 - 10*t^29 - 10*t^28 - 10*t^27 - 10*t^26 -
%F A170021 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 -
%F A170021 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 -
%F A170021 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4
%F A170021 - 10*t^3 - 10*t^2 - 10*t + 1)
%t A170021 coxG[{36,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 28 2015 *)
%K A170021 nonn
%O A170021 0,2
%A A170021 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009