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A163438
Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 13, 156, 1872, 22464, 269490, 3232944, 38784174, 465276240, 5581708704, 66961236342, 803303685756, 9636871221978, 115609188148740, 1386911174446512, 16638146470934274, 199600322709006648
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170732, 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)/(66*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
a(n) = 11*a(n-1)+11*a(n-2)+11*a(n-3)+11*a(n-4)-66*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6), {x, 0, 10}], x] (* or *) LinearRecurrence[{11, 11, 11, 11, -66}, {1, 13, 156, 1872, 22464, 269490}, 30]] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 66, -11}] (* 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)/(1-12*x+77*x^5-66*x^6)) \\ G. C. Greubel, Dec 23 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-12*x+77*x^5-66*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A162768 A097827 A163084 * A163958 A164610 A164815
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved