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A165788
Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845, 34867843200, 313810585200, 2824295234400, 25418656818000, 228767908737600, 2058911155018800, 18530200182592800, 166771799730147600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003952, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (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)/(36*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 10 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)) \\ G. C. Greubel, Sep 22 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11) )); // G. C. Greubel, Sep 22 2019
(Sage)
def A165788_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)).list()
A165788_list(20) # G. C. Greubel, Sep 22 2019
(GAP) a:=[10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845];; for n in [11..20] do a[n]:=8*Sum([1..9], j-> a[n-j]) -36*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019
CROSSREFS
Sequence in context: A164548 A164779 A165219 * A166368 A166543 A166933
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved