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A163317 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 6, 30, 150, 750, 3735, 18600, 92640, 461400, 2298000, 11445210, 57003000, 283904040, 1413987000, 7042377000, 35074632060, 174689570400, 870043225440, 4333259349600, 21581843340000, 107488595621160, 535348070440800 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003948, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
a(n) = 4*a(n-1)+4*a(n-2)+4*a(n-3)+4*a(n-4)-10*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 4, 4, 4, -10}, {1, 6, 30, 150, 750, 3735}, 30] (* G. C. Greubel, Dec 18 2016 *)
coxG[{5, 10, -4}] (* 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)/(1-5*x+14*x^5-10*x^6)) \\ G. C. Greubel, Dec 18 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-5*x+14*x^5-10*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A162937 A006818 A006819 * A342807 A163922 A164365
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)