A282969 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 1, 5, 5, 1, 2, 17, 38, 17, 2, 5, 75, 309, 309, 75, 5, 13, 295, 2012, 3635, 2012, 295, 13, 29, 1062, 12160, 35870, 35870, 12160, 1062, 29, 65, 3811, 70722, 346172, 577003, 346172, 70722, 3811, 65, 143, 13107, 395223, 3128641, 8716978

Offset

1,8

Comments

Table starts

...0.....0........0..........1............2..............5...............13

...0.....0........5.........17...........75............295.............1062

...0.....5.......38........309.........2012..........12160............70722

...1....17......309.......3635........35870.........346172..........3128641

...2....75.....2012......35870.......577003........8716978........124683166

...5...295....12160.....346172......8716978......206993155.......4646063540

..13..1062....70722....3128641....124683166.....4646063540.....163712015523

..29..3811...395223...27439857...1722329260...100644923252....5565122952951

..65.13107..2150350..234322382..23131988665..2119718238840..183787303136570

.143.44498.11454117.1959091067.303943320975.43654941219187.5933174659006889

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-3) -6*a(n-4) +4*a(n-6) +6*a(n-7) +3*a(n-8) +a(n-9)

k=2: [order 15]

k=3: [order 33]

k=4: [order 63]

Example

Some solutions for n=4 k=4
..0..0..1..0. .0..0..1..1. .0..0..1..0. .0..0..0..1. .1..0..1..0
..0..1..0..0. .1..0..0..0. .0..0..0..1. .1..1..1..0. .1..1..0..0
..1..0..1..0. .0..0..0..0. .1..1..1..0. .0..0..0..0. .0..0..0..0
..1..0..1..0. .1..1..1..1. .0..0..1..0. .1..0..1..1. .1..1..0..0

Crossrefs

Column 1 is A282831.

Sequence in context: A232651 A145227 A236555 * A046095 A322545 A256737

Adjacent sequences: A282966 A282967 A282968 * A282970 A282971 A282972

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 25 2017

Status

approved