A097554 Number of positive words of length n in the monoid Br_7 of positive braids on 8 strands.

1, 7, 36, 151, 570, 2019, 6893, 23034, 76020, 249077, 812614, 2644447, 8592693, 27895296, 90510106, 293576779, 952053411, 3087093728, 10009389358, 32452403488, 105214363653, 341111617862, 1105895184121, 3585328906357, 11623651559099

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 (7,-18,25,-24,15,-6,1).

Crossrefs

Cf. A097550, A097551, A097552, A097553, A097555, A097556.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x^2)^5/(1-7*x+18*x^2-25*x^3+24*x^4-15*x^5+6*x^6-x^7) )); // G. C. Greubel, Apr 20 2021

Mathematica

LinearRecurrence[{7,-18,25,-24,15,-6,1}, {1,7,36,151,570,2019,6893,23034,76020, 249077,812614}, 41] (* G. C. Greubel, Apr 20 2021 *)

Sage

def A097554_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^5/(1-7*x+18*x^2-25*x^3+24*x^4-15*x^5+6*x^6-x^7) ).list()
A097554_list(40) # G. C. Greubel, Apr 20 2021

Formula

G.f.: (1 +x^2)^5/(1 -7*x +18*x^2 -25*x^3 +24*x^4 -15*x^5 +6*x^6 -x^7).

Extensions

Corrected and extended by Max Alekseyev, Jun 17 2011