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

0,2

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).

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).

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 *)

Prog

(Magma)
R<x>:=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
(Sage)
def A097556_list(prec):
    P.<x> = 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

Crossrefs

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

Sequence in context: A242604 A212150 A203838 * A196861 A211844 A172065

Adjacent sequences: A097553 A097554 A097555 * A097557 A097558 A097559

Keyword

nonn,easy

Author

D n Verma, Aug 16 2004

Extensions

Edited and extended by Max Alekseyev, Jun 17 2011

Status

approved