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, 707584

Offset: 1

Author

R. H. Hardin, Jun 06 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A001250.

Cf. A008970, A059427.