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

1,3

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A214663.

Sequence in context: A213999 A374411 A249026 * A263905 A263693 A263714

Adjacent sequences: A263594 A263595 A263596 * A263598 A263599 A263600

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 22 2015

Status

approved