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A165266
Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
1
1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306506, 28295370840, 311249071320, 3423739697400, 37661135713080, 414272482302360, 4556997189369240, 50126967807537720, 551396631852151800
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003954, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (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)/(55*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 25 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), {t, 0, 30}], t] (* or *) coxG[{9, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 25 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)) \\ G. C. Greubel, Sep 25 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10) )); // G. C. Greubel, Sep 25 2019
(Sage)
def A165266_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)).list()
A165266_list(30) # G. C. Greubel, Sep 25 2019
(GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306506];; for n in [10..30] do a[n]:=10*Sum([1..8], j-> a[n-j]) -55*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 25 2019
CROSSREFS
Sequence in context: A063813 A164601 A164781 * A165807 A166372 A166557
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved