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A165796
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 10999999945, 109999998900, 1099999983555, 10999999781100, 109999997266500, 1099999967220000, 10999999617750000, 109999995633000000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003953, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
a(0) = a(1) = 1 (mod 5), a(n) = 0 (mod 5) for n>=2. - G. C. Greubel, Apr 08 2016
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)/(45*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 22 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 45, -9}] (* 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)/(1-10*t+54*t^10-45*t^11)) \\ G. C. Greubel, Sep 22 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11) )); // G. C. Greubel, Sep 22 2019
(Sage)
def A165796_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11)).list()
A165796_list(20) # G. C. Greubel, Sep 22 2019
(GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 10999999945];; for n in [11..20] do a[n]:=9*Sum([1..9], j-> a[n-j]) -45*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019
CROSSREFS
Sequence in context: A115830 A164780 A165264 * A166369 A166551 A166950
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved