A263666 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and with no two consecutive increases or two consecutive decreases.

1, 1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 4, 7, 2, 1, 2, 4, 10, 8, 2, 1, 2, 4, 10, 22, 12, 2, 1, 2, 4, 10, 32, 40, 16, 2, 1, 2, 4, 10, 32, 95, 70, 24, 2, 1, 2, 4, 10, 32, 122, 208, 133, 32, 2, 1, 2, 4, 10, 32, 122, 422, 486, 254, 48, 2, 1, 2, 4, 10, 32, 122, 544, 1222, 1064, 482, 64, 2, 1, 2, 4, 10, 32

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

.2..4...4....4....4.....4.....4.....4......4......4......4......4......4......4

.2..7..10...10...10....10....10....10.....10.....10.....10.....10.....10.....10

.2..8..22...32...32....32....32....32.....32.....32.....32.....32.....32.....32

.2.12..40...95..122...122...122...122....122....122....122....122....122....122

.2.16..70..208..422...544...544...544....544....544....544....544....544....544

.2.24.133..486.1222..2287..2770..2770...2770...2770...2770...2770...2770...2770

.2.32.254.1064.3302..7688.13102.15872..15872..15872..15872..15872..15872..15872

.2.48.482.2560.9021.25662.53324.86555.101042.101042.101042.101042.101042.101042

Links

R. H. Hardin, Table of n, a(n) for n = 1..484

Formula

Empirical for column k:

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

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

k=3: a(n) = 3*a(n-2) +2*a(n-4) for n>12

k=4: a(n) = 4*a(n-2) +6*a(n-4) +16*a(n-6) -8*a(n-10) for n>20

k=5: [order 22] for n>34

k=6: [order 52] for n>66

Example

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

Crossrefs

Diagonal is A001250.

Sequence in context: A350700 A178522 A131240 * A107027 A355395 A107030

Adjacent sequences: A263663 A263664 A263665 * A263667 A263668 A263669

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 23 2015

Status

approved