A263736 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 average of every three consecutive elements is never greater than the median of the previous three elements

1, 1, 2, 1, 2, 3, 1, 2, 6, 0, 1, 2, 6, 4, 0, 1, 2, 6, 14, 1, 0, 1, 2, 6, 14, 16, 0, 0, 1, 2, 6, 14, 38, 14, 0, 0, 1, 2, 6, 14, 38, 66, 0, 0, 0, 1, 2, 6, 14, 38, 127, 38, 0, 0, 0, 1, 2, 6, 14, 38, 127, 202, 9, 0, 0, 0, 1, 2, 6, 14, 38, 127, 411, 170, 6, 0, 0, 0, 1, 2, 6, 14, 38, 127, 411, 815, 115

Offset

1,3

Comments

Table starts

.1.1..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......2

.3.6..6..6...6....6....6.....6......6......6......6......6......6......6......6

.0.4.14.14..14...14...14....14.....14.....14.....14.....14.....14.....14.....14

.0.1.16.38..38...38...38....38.....38.....38.....38.....38.....38.....38.....38

.0.0.14.66.127..127..127...127....127....127....127....127....127....127....127

.0.0..0.38.202..411..411...411....411....411....411....411....411....411....411

.0.0..0..9.170..815.1492..1492...1492...1492...1492...1492...1492...1492...1492

.0.0..0..6.115.1166.3949..6478...6478...6478...6478...6478...6478...6478...6478

.0.0..0..0..26..561.5100.16569..27635..27635..27635..27635..27635..27635..27635

.0.0..0..0...1..303.3673.26714..82661.130093.130093.130093.130093.130093.130093

.0.0..0..0...0..297.4157.32419.181804.469245.695563.695563.695563.695563.695563

Links

R. H. Hardin, Table of n, a(n) for n = 1..483

Formula

Empirical for column k:

k=1: a(n) = a(n-1) for n>4

k=2: a(n) = a(n-1) for n>6

k=3: a(n) = a(n-1) for n>7

k=4: a(n) = a(n-1) for n>10

k=5: a(n) = a(n-1) for n>12

k=6: [order 39] for n>64

Example

Some solutions for n=7 k=4
..4....3....1....4....0....1....0....0....4....4....4....4....0....4....1....4
..0....5....5....1....5....5....5....5....0....0....1....0....5....0....3....1
..6....6....6....5....6....6....6....6....6....6....6....6....6....5....5....5
..5....4....4....3....4....3....4....1....5....5....5....5....4....6....0....6
..3....0....0....0....2....0....3....4....2....1....0....1....1....1....4....0
..1....1....3....6....1....2....1....3....1....3....3....2....2....3....6....2
..2....2....2....2....3....4....2....2....3....2....2....3....3....2....2....3

Crossrefs

Sequence in context: A343863 A263683 A087730 * A126247 A213999 A249026

Adjacent sequences: A263733 A263734 A263735 * A263737 A263738 A263739

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 25 2015

Status

approved