A283950 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 16, 87, 0, 0, 0, 84, 906, 900, 0, 0, 0, 408, 7988, 16648, 8184, 0, 0, 0, 1926, 69468, 264482, 283208, 71486, 0, 0, 0, 8776, 575456, 4242700, 8244557, 4510608, 597042, 0, 0, 0, 38912, 4604744, 64614384, 241796070, 242330064

Offset

1,8

Comments

Table starts

.0.0......0........0..........0............0..............0................0

.0.0......2.......16.........84..........408...........1926.............8776

.0.0.....87......906.......7988........69468.........575456..........4604744

.0.0....900....16648.....264482......4242700.......64614384........948567440

.0.0...8184...283208....8244557....241796070.....6763514843.....182198176994

.0.0..71486..4510608..242330064..13010689912...667015216686...32960788748780

.0.0.597042.68693470.6816984648.669777003928.62944601744067.5709831013093658

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 16]

k=4: [order 34]

k=5: [order 90]

Empirical for row n:

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

n=2: [order 8]

n=3: [order 28]

n=4: [order 56]

Example

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

Crossrefs

Sequence in context: A348029 A224074 A136615 * A342376 A277443 A209401

Adjacent sequences: A283947 A283948 A283949 * A283951 A283952 A283953

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 18 2017

Status

approved