cp's OEIS Frontend

A170319 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170319 #8 Jun 15 2022 12:35:38
%S A170319 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A170319 832102905942,17474161024782,366957381520422,7706105011928862,
%U A170319 161828205250506102,3398392310260628142,71366238515473190982
%N A170319 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170319 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A170319 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170319 <a href="/index/Rec#order_42">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, 20, 20, 20, 20, 20, 20, -210).
%F A170319 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170319 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170319 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170319 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170319 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 +
%F A170319 2*t + 1)/(210*t^42 - 20*t^41 - 20*t^40 - 20*t^39 - 20*t^38 - 20*t^37 -
%F A170319 20*t^36 - 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 -
%F A170319 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 -
%F A170319 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 -
%F A170319 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 -
%F A170319 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)
%t A170319 coxG[{42,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 15 2022 *)
%K A170319 nonn
%O A170319 0,2
%A A170319 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009