A097556 Number of positive words of length n in the monoid Br_9 of positive braids on 10 strands.

1, 9, 56, 279, 1223, 4932, 18833, 69345, 249166, 880525, 3076295, 10662459, 36749785, 126161246, 431880044, 1475412473, 5032964258, 17150277106, 58395929325, 198723871661, 675989712225, 2298799014859, 7815699898677, 26568450635871

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 (9,-32,63,-84,81,-56,27,-8,1).

Crossrefs

Cf. A097550, A097551, A097552, A097553, A097554, A097555.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( (1+x^2)^7/(1-9*x+32*x^2-63*x^3+84*x^4-81*x^5+56*x^6-27*x^7+8*x^8-x^9) )); // G. C. Greubel, Apr 20 2021

Mathematica

CoefficientList[Series[(1+x^2)^7/(1-9*x+32*x^2-63*x^3+84*x^4-81*x^5+56*x^6-27*x^7+8*x^8-x^9), {x,0,50}], x] (* G. C. Greubel, Apr 20 2021 *)

Sage

def A097556_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^7/(1-9*x+32*x^2-63*x^3+84*x^4-81*x^5+56*x^6-27*x^7+8*x^8-x^9) ).list()
A097556_list(50) # G. C. Greubel, Apr 20 2021

Formula

G.f.: (1 +x^2)^7/(1 -9*x +32*x^2 -63*x^3 +84*x^4 -81*x^5 +56*x^6 -27*x^7 +8*x^8 -x^9).

Extensions

Edited and extended by Max Alekseyev, Jun 17 2011