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A170463 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170463 #8 Jun 08 2021 17:02:49
%S A170463 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A170463 832102905942,17474161024782,366957381520422,7706105011928862,
%U A170463 161828205250506102,3398392310260628142,71366238515473190982
%N A170463 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170463 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A170463 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170463 <a href="/index/Rec#order_45">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, 20, 20, 20, -210).
%F A170463 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170463 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170463 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170463 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170463 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170463 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^45 - 20*t^44 - 20*t^43 -
%F A170463 20*t^42 - 20*t^41 - 20*t^40 - 20*t^39 - 20*t^38 - 20*t^37 - 20*t^36 -
%F A170463 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 -
%F A170463 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 -
%F A170463 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 -
%F A170463 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 -
%F A170463 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)
%t A170463 coxG[{45,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 08 2021 *)
%K A170463 nonn
%O A170463 0,2
%A A170463 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009