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A163404
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 11, 110, 1100, 11000, 109945, 1098900, 10983555, 109781100, 1097266500, 10967222970, 109617836625, 1095634704780, 10950913128375, 109454819042250, 1094005337374620, 10934627535602100, 109292043884611005
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^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
a(n) = 9*a(n-1)+9*a(n-2)+9*a(n-3)+9*a(n-4)-45*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1 + x)*(1-x^5)/(1-10*x+54*x^5-45*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{9, 9, 9, 9, -45}, {1, 11, 110, 1100, 11000, 109945}, 30]] (* G. C. Greubel, Dec 21 2016 *)
coxG[{5, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6)) \\ G. C. Greubel, Dec 21 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-10*x+54*x^5-45*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A121031 A115804 A162987 * A115808 A163955 A164590
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved