cp's OEIS Frontend

A169563 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169563 #8 Jun 07 2018 15:39:07
%S A169563 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A169563 832102905942,17474161024782,366957381520422,7706105011928862,
%U A169563 161828205250506102,3398392310260628142,71366238515473190982
%N A169563 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169563 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A169563 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169563 <a href="/index/Rec#order_35">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, -210).
%F A169563 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169563 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169563 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169563 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
%F A169563 + 2*t^2 + 2*t + 1)/(210*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 -
%F A169563 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 -
%F A169563 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 -
%F A169563 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 -
%F A169563 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 -
%F A169563 20*t + 1)
%t A169563 coxG[{35,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 07 2018 *)
%K A169563 nonn
%O A169563 0,2
%A A169563 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009