cp's OEIS Frontend

A170031 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170031 #8 Nov 26 2016 09:43:13
%S A170031 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A170031 832102905942,17474161024782,366957381520422,7706105011928862,
%U A170031 161828205250506102,3398392310260628142,71366238515473190982
%N A170031 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170031 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A170031 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170031 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A170031 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 A170031 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 A170031 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 A170031 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 A170031 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^36 - 20*t^35 - 20*t^34 - 20*t^33 -
%F A170031 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 -
%F A170031 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 -
%F A170031 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 -
%F A170031 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4
%F A170031 - 20*t^3 - 20*t^2 - 20*t + 1)
%t A170031 coxG[{36,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 14 2015 *)
%K A170031 nonn
%O A170031 0,2
%A A170031 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009