A234282 Number of 321-avoiding extensions of comb K_{s,2}^{alpha}.

1, 3, 13, 67, 378, 2244, 13737, 85767, 542685, 3466515, 22298796, 144210388, 936575968

Offset

1,2

Comments

No formula is presently known.

From Colin Defant, Aug 16 2016: (Start)

For each subset W={w_1,w_2,...,w_k} of {n+1,n+2,...,2n} satisfying w_1<w_2<...<w_k, let H(W) be the number of sequences of integers i_1,i_2,...,i_k such that i_1<i_2<...<i_k and w_j-n+j<=i_j<=w_j-1 for all j. We have a(n)=Sum(H(W)), where the sum ranges over all subsets W of {n+1,n+2,...,2n}.

3 + sqrt(8) <= lim_(n->oo)a(n)^(1/n) <= 27/4. (End)

Links

Table of n, a(n) for n=1..13.

C. Defant, Some Poset Pattern-Avoidance Problems Posed by Yakoubov, arXiv:1608.03951 [math.CO], 2016.

S. Yakoubov, Pattern Avoidance in Extensions of Comb-Like Posets, arXiv preprint arXiv:1310.2979 [math.CO], 2013.

Crossrefs

Sequence in context: A027277 A242798 A239198 * A366011 A365250 A200754

Adjacent sequences: A234279 A234280 A234281 * A234283 A234284 A234285

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 28 2013

Extensions

a(7)-a(13) from Colin Defant, Aug 16 2016

Status

approved