A166377 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734834, 9659108817072, 115909305793710, 1390911669390672, 16690940031081888, 200291280353708544
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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12) )); // G. C. Greubel, Apr 25 2019 -
Mathematica
CoefficientList[Series[(1+t)*(1-t^11)/(1-12*t+77*t^11-66*t^12), {t, 0, 20}], t] (* G. C. Greubel, May 10 2016 *) -
PARI
my(x='x+O('x^20)); Vec((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)) \\ G. C. Greubel, Apr 25 2019 -
Sage
((1+x)*(1-x^11)/(1-12*x+77*x^11-66*x^12)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
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)/(66*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
G.f.: (1 + t - t^11 - t^12)/(1 - 12*t + 77*t^11 - 66*t^12). - Zak Seidov, Dec 05 2009
Comments