A166416 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520191, 7706105011919160, 161828205250200720, 3398392310252080680, 71366238515248871040
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (20,20,20,20,20,20,20,20,20,20,-210).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^11)/(1-21*x+230*x^11-210*x^12) )); // G. C. Greubel, Jul 23 2024 -
Mathematica
With[{p=210, q=20}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t,0,40}], t]] (* G. C. Greubel, May 13 2016; Jul 23 2024 *) coxG[{11, 210, -20, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 23 2024 *)
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SageMath
def A166416_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( (1+x)*(1-x^11)/(1-21*x+230*x^11-210*x^12) ).list() A166416_list(30) # G. C. Greubel, Jul 23 2024
Formula
G.f.: (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^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).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 20*Sum_{j=1..10} a(n-j) - 210*a(n-11).
G.f.: (1+x)*(1 - x^11)/(1 - 21*x + 230*x^11 - 210*x^12). (End)
Comments