A316763 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 4, 18, 0, 0, 61, 46, 46, 61, 0, 0, 209, 151, 410, 151, 209, 0, 0, 702, 543, 2397, 2397, 543, 702, 0, 0, 2381, 2120, 13970, 26845, 13970, 2120, 2381, 0, 0, 8069, 8155, 93426, 219766, 219766, 93426, 8155, 8069, 0, 0, 27330, 30205, 586718

Offset

1,5

Comments

Table starts

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

.0....3.....5......18........61........209..........702...........2381

.0....5.....4......46.......151........543.........2120...........8155

.0...18....46.....410......2397......13970........93426.........586718

.0...61...151....2397.....26845.....219766......2442827.......24591846

.0..209...543...13970....219766....2605126.....42857655......625815905

.0..702..2120...93426...2442827...42857655...1169271436....26888275330

.0.2381..8155..586718..24591846..625815905..26888275330...947123604065

.0.8069.30205.3677924.242436003.9056077433.613862574233.33009635701375

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) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

k=3: [order 18]

k=4: [order 66] for n>67

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..1..1..0..0. .0..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..0..0
..0..0..0..1. .0..0..0..0. .0..0..1..0. .1..1..0..0. .1..0..1..0
..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..1
..1..1..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..1..0

Crossrefs

Column 2 is A303684.

Column 3 is A305170.

Column 4 is A305171.

Sequence in context: A304156 A305509 A305175 * A304065 A305457 A305022

Adjacent sequences: A316760 A316761 A316762 * A316764 A316765 A316766

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 12 2018

Status

approved