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A163345
Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 7, 42, 252, 1512, 9051, 54180, 324345, 1941660, 11623500, 69582660, 416548125, 2493614550, 14927719275, 89362970550, 534960522600, 3202475913000, 19171231408875, 114766238286000, 687034086094125, 4112845750671000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003949, 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)/(15*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
a(n) = 5*a(n-1)+5*a(n-2)+5*a(n-3)+5*a(n-4)-15*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 5, 5, 5, -15}, {1, 7, 42, 252, 1512, 9051}, 30] (* G. C. Greubel, Dec 19 2016 *)
coxG[{5, 15, -5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 09 2018 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6)) \\ G. C. Greubel, Dec 19 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-6*x+20*x^5-15*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A214941 A162941 A094168 * A163923 A164369 A164742
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved