A097551 Number of positive words of length n in the monoid Br_4 of positive braids on 5 strands.

1, 4, 13, 37, 101, 273, 737, 1990, 5374, 14513, 39194, 105848, 285855, 771985, 2084836, 5630344, 15205404, 41063976, 110898081, 299493268, 808816679, 2184304257, 5898969706, 15930859211, 43023152830, 116189067703

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,5,-3,1).

Formula

G.f.: (1 + x^2)^2/(1 - 4*x + 5*x^2 - 5*x^3 + 3*x^4 - x^5).

Mathematica

<<DiscreteMath`; Do[Print[SeriesTerm[(1 + q^2)^2/(1-4q+5q^2-5q^3+3q^4-q^5), {q, 0, n}]], {n, 0, 50}] (* Ryan Propper, Sep 27 2005 *)
LinearRecurrence[{4, -5, 5, -3, 1}, {1, 4, 13, 37, 101}, 51] (* G. C. Greubel, Apr 19 2021 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( (1+x^2)^2/(1-4*x+5*x^2-5*x^3+3*x^4-x^5) )); // G. C. Greubel, Apr 19 2021
(Sage)
def A097551_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^2/(1-4*x+5*x^2-5*x^3+3*x^4-x^5) ).list()
A097551_list(50) # G. C. Greubel, Apr 19 2021

Crossrefs

Cf. A097550, A097552, A097553, A097554, A097555, A097556.

Sequence in context: A244197 A300985 A080145 * A224033 A095126 A077842

Adjacent sequences: A097548 A097549 A097550 * A097552 A097553 A097554

Keyword

nonn,easy

Author

D n Verma, Aug 16 2004

Extensions

More terms from Ryan Propper, Sep 27 2005

Status

approved