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A097552 Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands. 7
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 (list; graph; refs; listen; history; text; internal format)
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 (5,-8,7,-4,1).

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

MATHEMATICA

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

PROG

(Magma)

R<x>:=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

(Sage)

def A097552_list(prec):

    P.<x> = 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

CROSSREFS

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

Sequence in context: A271066 A271599 A032286 * A322600 A084850 A270169

Adjacent sequences:  A097549 A097550 A097551 * A097553 A097554 A097555

KEYWORD

nonn,easy

AUTHOR

D n Verma, Aug 16 2004

EXTENSIONS

Corrected by T. D. Noe, Nov 02 2006

STATUS

approved

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Last modified May 21 09:30 EDT 2022. Contains 353908 sequences. (Running on oeis4.)