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A108600 Number of freely braided permutations of length n; the freely braided permutations are those that avoid 3421, 4231, 4312 and 4321. 3
1, 2, 6, 20, 71, 260, 971, 3674, 14032, 53968, 208692, 810492, 3158760, 12346628, 48377494, 189952216, 747180999, 2943648824, 11612917815, 45869337526, 181372345723, 717856746216, 2843678131629, 11273602645942, 44725291921541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. M. Green and J. Losonczy, Freely braided elements of Coxeter groups, Ann. Comb. 6 (2002), 337-348.

T. Mansour, On an open problem of Green and Losonczy: exact enumeration of freely braided permutations, Discrete Math. Comput. Sci. 6 (2004), 461-470.

LINKS

Table of n, a(n) for n=1..25.

V. Vatter, Enumeration scheme for freely braided permutations.

FORMULA

G.f. (1-3*x-2*x^2+(1+x)*sqrt(1-4*x)) / (1-4*x-x^2+(1-x^2)*sqrt(1-4*x)).

Conjecture: (1-n)*a(n) +(7*n-10)*a(n-1) +2*(1-4*n)*a(n-2) +8*(11-2*n)*a(n-3) +(n-1)*a(n-4) +3*(2-n)*a(n-5) +2*(11-2*n)*a(n-6)=0. - R. J. Mathar, Aug 24 2013

EXAMPLE

a(5)=71 because there are 71 permutations of length 5 that avoid 3421, 4231, 4312 and 4321.

CROSSREFS

Sequence in context: A145138 A000707 A129777 * A274484 A128729 A006027

Adjacent sequences:  A108597 A108598 A108599 * A108601 A108602 A108603

KEYWORD

easy,nonn

AUTHOR

Vincent Vatter, Jun 11 2005

STATUS

approved

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Last modified May 23 04:59 EDT 2019. Contains 323508 sequences. (Running on oeis4.)