A052978 -id:A052978 - cp's OEIS frontend

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

R. H. Hardin, Dec 17 2012

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

			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

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

Columns k=1-10 give: A000045(n+1), A052978, A220639, A220640, A220641, A220642, A220643, A243314, A243315, A243316.
Main diagonal is A220638.
Cf. A239264.

cp's OEIS Frontend

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.

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