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A169419 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169419 #14 Jul 16 2018 11:10:02
%S A169419 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A169419 832102905942,17474161024782,366957381520422,7706105011928862,
%U A169419 161828205250506102,3398392310260628142,71366238515473190982
%N A169419 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169419 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A169419 First disagreement is at index 32, the difference is 231. - _Klaus Brockhaus_, Jun 27 2011
%C A169419 Computed with Magma using commands similar to those used to compute A154638.
%H A169419 <a href="/index/Rec#order_32">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, -210).
%F A169419 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%F A169419 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-20*sum(k=1..31, x^k)+210*x^32).
%t A169419 coxG[{32,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 16 2018 *)
%Y A169419 Cf. A170741 (G.f.: (1+x)/(1-21*x) ).
%K A169419 nonn
%O A169419 0,2
%A A169419 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009