A220644 T(n,k) = number of ways to reciprocally link elements of an n X k array either to themselves or to exactly one king-move neighbor.

1, 2, 2, 3, 10, 3, 5, 40, 40, 5, 8, 172, 369, 172, 8, 13, 728, 3755, 3755, 728, 13, 21, 3096, 37320, 92801, 37320, 3096, 21, 34, 13152, 373177, 2226936, 2226936, 373177, 13152, 34, 55, 55888, 3725843, 53841725, 128171936, 53841725, 3725843, 55888, 55, 89

Offset

1,2

Comments

Table starts

...1........2............3.................5.....................8

...2.......10...........40...............172...................728

...3.......40..........369..............3755.................37320

...5......172.........3755.............92801...............2226936

...8......728........37320...........2226936.............128171936

..13.....3096.......373177..........53841725............7444342896

..21....13152......3725843........1299348473..........431408410784

..34....55888.....37213728.......31371388772........25014514225856

..55...237472....371654153......757341382671......1450226501771584

..89..1009056...3711809483....18283618480037.....84080327982982848

.144..4287616..37070598992...441397115736816...4874715696405194752

.233.18218688.370232236753.10656083384666537.282621433306639435392

Links

Alois P. Heinz, Table of n, a(n) for n = 1..528 (antidiagonals 1..32) (terms n = 1..180 from R. H. Hardin)

Example

Some solutions for n=3 k=4 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
..0..6..4..8....6..4..0..0....8..0..0..0....9..6..4..8....6..4..0..0
..0..7..7..2....8..0..9..7....2..8..8..0....8..1..9..2....0..0..8..8
..3..3..6..4....2..0..3..1....0..2..2..0....2..6..4..1....0..0..2..2

Crossrefs

Columns k=1-10 give: A000045(n+1), A052978, A220639, A220640, A220641, A220642, A220643, A243314, A243315, A243316.

Main diagonal is A220638.

Cf. A239264.

Sequence in context: A032103 A091044 A079661 * A338372 A153920 A300483

Adjacent sequences: A220641 A220642 A220643 * A220645 A220646 A220647

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2012

Status

approved