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A165515
Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
1
1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395, 435214379250840, 12621216997908960, 366015292928763240, 10614443494626832560, 307818861335266403640, 8926746978464285228160
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170749, 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)/( 406*t^9 -28*t^8 -28*t^7 -28*t^6 -28*t^5 -28*t^4 -28*t^3 -28*t^2 -28*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 16 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), {t, 0, 20}], t] (* G. C. Greubel, Oct 21 2018 *)
coxG[{9, 406, -28}] (* 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)/(1-29*t+434*t^9-406*t^10)) \\ G. C. Greubel, Oct 21 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10) )); // G. C. Greubel, Oct 21 2018
(Sage)
def A165515_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)).list()
A165515_list(20) # G. C. Greubel, Sep 16 2019
(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395];; for n in [10..20] do a[n]:=28*Sum([1..8], j-> a[n-j]) -406*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019
CROSSREFS
Sequence in context: A164027 A164666 A164983 * A166026 A166424 A166617
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved