A097552 Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands.

1, 5, 20, 67, 209, 630, 1873, 5540, 16357, 48265, 142387, 420027, 1239006, 3654820, 10780958, 31801551, 93807834, 276713194, 816245143, 2407749755, 7102350204, 20950424039, 61799299470, 182294802589, 537730934397

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 (5,-8,7,-4,1).

Crossrefs

Cf. A097550, A097551, A097553, A097554, A097555, A097556.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) )); // G. C. Greubel, Apr 19 2021

Mathematica

LinearRecurrence[{5,-8,7,-4,1}, {1,5,20,67,209,630,1873}, 40] (* G. C. Greubel, Apr 19 2021 *)

Sage

def A097552_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) ).list()
A097552_list(40) # G. C. Greubel, Apr 19 2021

Formula

G.f.: (1 + x^2)^3/(1 - 5*x + 8*x^2 - 7*x^3 + 4*x^4 - x^5). - T. D. Noe, Nov 02 2006

Extensions

Corrected by T. D. Noe, Nov 02 2006