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A165512
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
1
1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951338, 306775222626096, 8589706233212790, 240511774521056976, 6734329686340363296, 188561231210551675392, 5279714473700048997888
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170748, 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)/(378*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 16 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 21 2018 *)
coxG[{9, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10)) \\ G. C. Greubel, Oct 21 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10) )); // G. C. Greubel, Oct 21 2018
(Sage)
def A165512_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^9)/(1-28*t+405*t^9-378*t^10)).list()
A165512_list(20) # G. C. Greubel, Sep 16 2019
(GAP) a:=[29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951338];; for n in [10..20] do a[n]:=27*Sum([1..8], j-> a[n-j]) -378*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019
CROSSREFS
Sequence in context: A164026 A164665 A164974 * A166004 A166423 A166616
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved