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A162760
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
1
1, 11, 110, 1045, 9900, 93555, 884070, 8353125, 78924780, 745717995, 7045894350, 66572896005, 629011803420, 5943197049075, 56154099352230, 530570136457845, 5013074255082300, 47365865053010955, 447534797632236270
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.
FORMULA
G.f.: (t^3 + 2*t^2 + 2*t + 1)/(45*t^3 - 9*t^2 - 9*t + 1).
G.f.: (1+x)*(1-x^3)/(1 - 10*x + 54*x^3 - 45*x^4). - G. C. Greubel, Apr 26 2019
MATHEMATICA
Join[{1}, LinearRecurrence[{9, 9, -45}, {11, 110, 1045}, 19]] (* Vincenzo Librandi, Apr 01 2017 *)
CoefficientList[Series[(1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4), {x, 0, 20}], x] (* or *) coxG[{3, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)
PROG
(Magma) I:=[1, 11, 110, 1045]; [n le 4 select I[n] else 9*Self(n-1) +9*Self(n-2)-45*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4) )); // G. C. Greubel, Apr 26 2019
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)) \\ G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
CROSSREFS
Sequence in context: A132123 A190944 A115822 * A190871 A097784 A352574
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved