A264336 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,1 1,0 1,-1 or 0,-1.

0, 1, 1, 1, 2, 1, 1, 4, 4, 1, 2, 8, 11, 8, 2, 3, 16, 40, 40, 16, 3, 4, 32, 133, 240, 133, 32, 4, 6, 64, 464, 1528, 1528, 464, 64, 6, 9, 128, 1573, 8976, 15040, 8976, 1573, 128, 9, 13, 256, 5373, 51904, 144289, 144289, 51904, 5373, 256, 13, 19, 512, 18376, 302328, 1371555

Offset

1,5

Comments

Table starts

..0...1.....1........1..........2............3..............4................6

..1...2.....4........8.........16...........32.............64..............128

..1...4....11.......40........133..........464...........1573.............5373

..1...8....40......240.......1528.........8976..........51904...........302328

..2..16...133.....1528......15040.......144289........1371555.........13030122

..3..32...464.....8976.....144289......2464988.......40119900........640302232

..4..64..1573....51904....1371555.....40119900.....1082465413......28865247648

..6.128..5373...302328...13030122....640302232....28865247648....1305850666324

..9.256.18376..1757848..123154946..10206221300...765329377660...57981524413360

.13.512.62754.10199400.1162675576.162325629616.20139599598080.2544934124095448

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3)

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

k=3: [order 14]

k=4: a(n) = 6*a(n-1) -5*a(n-2) +36*a(n-3) -72*a(n-4) -243*a(n-6) for n>7

k=5: [order 84]

k=6: [order 36] for n>38

Example

Some solutions for n=4 k=4
..1..5..3..4..8....1..2..6..7..8....1..2..6..7..8....1..2..6..4..8
..0..7..2.12.13....0.10..3.12..4....0.10.11..3..4....0.10..3.12.13
.11..6.16..9.18....5.15.16.14..9....5.12.13.14..9....5.15..7.17..9
.10.20.21.14.23...11.20.13.22.23...16.20.21.22.23...11.20.18.22.14
.15.22.17.24.19...21.17.18.24.19...15.17.18.24.19...21.16.23.24.19

Crossrefs

Column 1 is A000930(n-2).

Column 2 is A000079(n-1).

Sequence in context: A119732 A260625 A306614 * A350012 A322038 A123521

Adjacent sequences: A264333 A264334 A264335 * A264337 A264338 A264339

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 11 2015

Status

approved