A097553 Number of positive words of length n in the monoid Br_6 of positive braids on 7 strands.

1, 6, 27, 101, 346, 1131, 3611, 11396, 35761, 111906, 349700, 1092039, 3409031, 10640179, 33206991, 103631414, 323402952, 1009233980, 3149469548, 9828376731, 30670834516, 95712596642, 298684343689, 932085486213, 2908700435744

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 (6,-13,17,-17,11,-5,1).

Crossrefs

Cf. A097550, A097551, A097552, A097554, A097555, A097556.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( (1+x^2)^4/(1-6*x+13*x^2-17*x^3+17*x^4-11*x^5+5*x^6-x^7) )); // G. C. Greubel, Apr 20 2021

Mathematica

CoefficientList[Series[(1+n^2)^4/(1-6n+13n^2-17n^3+17n^4-11n^5+5n^6-n^7),{n,0,30}],n] (* Harvey P. Dale, Sep 27 2019 *)
LinearRecurrence[{6,-13,17,-17,11,-5,1}, {1,6,27,101,346,1131,3611,11396,35761}, 40] (* G. C. Greubel, Apr 20 2021 *)

Sage

def A097553_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^4/(1-6*x+13*x^2-17*x^3+17*x^4-11*x^5+5*x^6-x^7) ).list()
A097553_list(50) # G. C. Greubel, Apr 20 2021

Formula

G.f.: (1 +x^2)^4/(1 -6*x +13*x^2 -17*x^3 +17*x^4 -11*x^5 +5*x^6 -x^7).

Extensions

Corrected and extended by Max Alekseyev, Jun 17 2011