A097555 Number of positive words of length n in the monoid Br_8 of positive braids on 9 strands.

1, 8, 45, 205, 831, 3133, 11294, 39585, 136302, 464026, 1568151, 5273999, 17681042, 59149925, 197598856, 659479754, 2199585548, 7333198205, 24441067317, 81444567492, 271360676916, 904051477063, 3011711782025, 10032660556567, 33420042561972

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 (8,-25,45,-59,57,-41,21,-7,1).

Crossrefs

Cf. A097550, A097551, A097552, A097553, A097554, A097556.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x^2)^6 /(1-8*x+25*x^2-45*x^3+59*x^4-57*x^5+41*x^6-21*x^7+7*x^8-x^9) )); // G. C. Greubel, Apr 20 2021

Mathematica

LinearRecurrence[{8,-25,45,-59,57,-41,21,-7,1}, {1,8,45,205,831,3133,11294,39585, 136302, 464026, 1568151, 5273999, 17681042}, 41] (* G. C. Greubel, Apr 20 2021 *)

Sage

def A097555_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^6 /(1-8*x+25*x^2-45*x^3+59*x^4-57*x^5+41*x^6-21*x^7+7*x^8-x^9) ).list()
A097555_list(40) # G. C. Greubel, Apr 20 2021

Formula

G.f.: (1 +x^2)^6 /(1 -8*x +25*x^2 -45*x^3 +59*x^4 -57*x^5 +41*x^6 -21*x^7 +7*x^8 -x^9).

Extensions

Edited and extended by Max Alekseyev, Jun 17 2011