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
References
- N. Shar, Experimental methods in permutation patterns and bijective proof, PhD thesis, Rutgers University (2016)
Crossrefs
Cf. A217193.
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).
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