A271648 Number of permutations in S_{2*n+3} containing the pattern 2143...(2n)(2n-1).

6, 119, 2279, 18042, 83921, 284428, 782795, 1859374, 3957717, 7738336, 14140143, 24449570, 40377369, 64143092, 98567251, 147171158, 214284445, 305160264, 426098167, 584574666, 789381473, 1050771420

Offset

0,1

Comments

This sequence is eventually polynomial.

References

N. Shar, Experimental methods in permutation patterns and bijective proof, PhD thesis, Rutgers University (2016)

Links

Table of n, a(n) for n=0..21.

Formula

For n >= 2, a(n) = (32/3)*n^6 + 32*n^5 + (80/3)*n^4 + (16/3)*n^3 + 38/3*n^2 + 59/3*n + 13 (conjectured).

Conjectures from Colin Barker, Apr 11 2016: (Start)

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) for n>6.

G.f.: (6+77*x+1572*x^2+4378*x^3+1531*x^4+137*x^5-22*x^6+x^8) / (1-x)^7.

(End)

Remark by Nathaniel Shar, Apr 13 2016: The preceding three conjectures are equivalent (provided appropriate initial conditions are specified for the recurrence relation).

Crossrefs

Cf. A217193.

Sequence in context: A218713 A360426 A054957 * A353691 A290341 A246827

Adjacent sequences: A271645 A271646 A271647 * A271649 A271650 A271651

Keyword

nonn,easy

Author

Nathaniel Shar, Apr 11 2016

Status

approved