A129776 Number of maximally-clustered hexagon-avoiding permutations in S_n; the maximally-clustered hexagon-avoiding permutations are those that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234.

1, 2, 6, 21, 78, 298, 1157, 4535, 17872, 70644, 279704, 1108462, 4395045, 17431206, 69144643, 274300461, 1088215370, 4317321235, 17128527716, 67956202025, 269612504850, 1069675361622, 4243893926396, 16837490364983, 66802139457897, 265035151393777

Offset

1,2

Comments

If w is maximally-clustered and hexagon-avoiding, there are simple explicit formulas for all the Kazhdan-Lusztig polynomials P_{x,w}.

References

Jozsef Losonczy, Maximally clustered elements and Schubert varieties, Ann. Comb. 11 (2007), no. 2, 195-212.

Links

Table of n, a(n) for n=1..26.

H. Denoncourt and B. Jones, The enumeration of maximally clustered permutations.

B. Jones, Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations.

Formula

G.f.: (3x^6+x^5-5x^4+7x^3-5x^2+x) / (-3x^6+4x^5+8x^4-14x^3+15x^2-7x+1).

Example

a(8)=4535 because there are 4535 permutations of size 8 that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234 and 56781234.

Prog

(PARI) lista(nt) = { my(x = 'x + 'x*O('x^nt) ); P = (3*x^6+x^5-5*x^4+7*x^3-5*x^2+x) / (-3*x^6+4*x^5+8*x^4-14*x^3+15*x^2-7*x+1); print(Vec(P)); } \\ Michel Marcus, Mar 17 2013

Crossrefs

Cf. A058094, A108600.

Sequence in context: A124292 A277221 A360168 * A129775 A235391 A254316

Adjacent sequences: A129773 A129774 A129775 * A129777 A129778 A129779

Keyword

nonn

Author

Brant Jones (brant(AT)math.washington.edu), May 17 2007

Extensions

More terms from Michel Marcus, Mar 17 2013

Status

approved