A263597 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the median of every three consecutive elements nondecreasing.

1, 1, 2, 1, 2, 3, 1, 2, 6, 5, 1, 2, 6, 12, 8, 1, 2, 6, 16, 25, 13, 1, 2, 6, 16, 41, 57, 21, 1, 2, 6, 16, 52, 108, 124, 34, 1, 2, 6, 16, 52, 164, 280, 268, 55, 1, 2, 6, 16, 52, 208, 476, 729, 588, 89, 1, 2, 6, 16, 52, 208, 676, 1428, 1908, 1285, 144, 1, 2, 6, 16, 52, 208, 800, 2208, 4308

Offset: 1

Author

R. H. Hardin, Oct 22 2015

Keywords

• nonn
• tabl

Comments

Table starts

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

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

..3....6....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6.....6

..5...12...16....16....16....16....16....16....16....16....16....16....16....16

..8...25...41....52....52....52....52....52....52....52....52....52....52....52

.13...57..108...164...208...208...208...208...208...208...208...208...208...208

.21..124..280...476...676...800...800...800...800...800...800...800...800...800

.34..268..729..1428..2208..2900..3360..3360..3360..3360..3360..3360..3360..3360

.55..588.1908..4308..7696.10960.14024.16224.16224.16224.16224.16224.16224.16224

.89.1285.4969.12816.25508.40792.55492.69212.78088.78088.78088.78088.78088.78088

Examples

			Some solutions for n=6 k=4
..1....1....1....0....2....0....0....0....1....4....3....2....1....4....0....2
..2....2....0....1....1....5....3....1....5....1....1....0....4....0....1....0
..3....3....2....3....5....2....2....2....0....0....0....1....0....1....3....1
..0....0....4....4....3....3....1....5....2....2....2....5....3....3....5....3
..4....5....3....2....0....4....4....3....4....3....4....3....5....2....2....4
..5....4....5....5....4....1....5....4....3....5....5....4....2....5....4....5
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..516

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A214663.

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)

k=3: a(n) = a(n-1) +a(n-2) +7*a(n-3) +2*a(n-4) +4*a(n-5) -a(n-7) -a(n-8)

k=4: [order 15]

k=5: [order 31]

k=6: [order 67]