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

Author

D n Verma, Aug 16 2004

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

R:=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

Mathematica

<Ryan Propper, Sep 27 2005 *)
LinearRecurrence[{4,-5,5,-3,1}, {1,4,13,37,101}, 51] (* G. C. Greubel, Apr 19 2021 *)

Sage

def A097551_list(prec):
    P. = 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

Formula

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

Extensions

More terms from Ryan Propper, Sep 27 2005