A283784 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 0, 5, 1, 0, 0, 14, 60, 6, 0, 0, 113, 625, 745, 49, 0, 0, 564, 5432, 10910, 7298, 272, 0, 0, 2410, 43793, 169426, 174447, 62303, 1376, 0, 0, 10648, 336614, 2343698, 4588054, 2510456, 496884, 6620, 0, 0, 45070, 2456405, 30330979

Offset

1,8

Comments

Table starts

.0.....0........0..........0.............0...............0.................0

.0.....0........5.........14...........113.............564..............2410

.0.....1.......60........625..........5432...........43793............336614

.0.....6......745......10910........169426.........2343698..........30330979

.0....49.....7298.....174447.......4588054.......109281786........2393467823

.0...272....62303....2510456.....112397437......4572654404......169720104148

.0..1376...496884...33933330....2592339953....179632502674....11308125156356

.0..6620..3767599..439118692...57256730323...6737192690688...719819137224851

.0.30552.27544383.5498459845.1224525471560.244126676935480.44286142978155009

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

k=2: [order 15]

k=3: [order 30]

k=4: [order 42]

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: [order 15]

n=3: [order 33]

n=4: [order 69]

Example

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

Crossrefs

Column 2 is A283226.

Sequence in context: A204619 A228077 A204170 * A361353 A281563 A293087

Adjacent sequences: A283781 A283782 A283783 * A283785 A283786 A283787

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 16 2017

Status

approved