A226441 T(n,k)=Number of permutations of 1..n with fewer than k interior elements having values lying between the values of their neighbors

1, 1, 2, 1, 2, 4, 1, 2, 6, 10, 1, 2, 6, 22, 32, 1, 2, 6, 24, 90, 122, 1, 2, 6, 24, 118, 422, 544, 1, 2, 6, 24, 120, 658, 2226, 2770, 1, 2, 6, 24, 120, 718, 4078, 13102, 15872, 1, 2, 6, 24, 120, 720, 4914, 27724, 85170, 101042, 1, 2, 6, 24, 120, 720, 5038, 37300, 205134, 606542

Offset

1,3

Comments

Table starts

.......1........1.........1.........1.........1.........1.........1.........1

.......2........2.........2.........2.........2.........2.........2.........2

.......4........6.........6.........6.........6.........6.........6.........6

......10.......22........24........24........24........24........24........24

......32.......90.......118.......120.......120.......120.......120.......120

.....122......422.......658.......718.......720.......720.......720.......720

.....544.....2226......4078......4914......5038......5040......5040......5040

....2770....13102.....27724.....37300.....40066.....40318.....40320.....40320

...15872....85170....205134....308460....353556....362370....362878....362880

..101042...606542...1641534...2748354...3399246...3600306...3627778...3628798

..707584..4697946..14132390..26194542..35142546..38963958..39830282..39914754

.5405530.39330982.130299584.265691456.387129588.453658380.475089392.478739984

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Example

Some solutions for n=8 k=4
..5....8....1....7....5....5....8....4....7....5....3....4....7....6....5....1
..8....1....7....3....1....4....1....7....2....4....5....2....2....5....3....2
..6....5....2....6....3....8....7....5....1....3....7....1....5....4....7....7
..7....6....6....8....6....6....6....1....5....8....2....7....1....7....6....4
..3....7....3....2....7....3....3....3....6....1....6....5....8....1....1....3
..4....3....8....1....4....7....2....8....4....7....4....8....3....8....2....6
..1....4....5....5....8....2....5....6....3....6....1....6....4....3....4....8
..2....2....4....4....2....1....4....2....8....2....8....3....6....2....8....5

Crossrefs

Column 1 is A001250

Sequence in context: A114791 A129994 A208755 * A080246 A113413 A333571

Adjacent sequences: A226438 A226439 A226440 * A226442 A226443 A226444

Keyword

nonn,tabl

Author

R. H. Hardin Jun 06 2013

Status

approved