A304767 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 16, 18, 0, 0, 61, 103, 103, 61, 0, 0, 209, 609, 1321, 609, 209, 0, 0, 702, 3680, 14831, 14831, 3680, 702, 0, 0, 2381, 22187, 172574, 316639, 172574, 22187, 2381, 0, 0, 8069, 133917, 1999511, 6978743, 6978743, 1999511

Offset

1,5

Comments

Table starts

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

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

.0....5.....16.......103.........609...........3680............22187

.0...18....103......1321.......14831.........172574..........1999511

.0...61....609.....14831......316639........6978743........153265405

.0..209...3680....172574.....6978743......292676592......12219307955

.0..702..22187...1999511...153265405....12219307955.....969267512820

.0.2381.133917..23203301..3370551763...510976436144...77018325396680

.0.8069.808316.269239457.74123574757.21366609684109.6119460744287122

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 13] for n>15

k=4: [order 31] for n>32

Example

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

Crossrefs

Column 2 is A303684.

Sequence in context: A305457 A305022 A316686 * A316511 A317465 A051174

Adjacent sequences: A304764 A304765 A304766 * A304768 A304769 A304770

Keyword

nonn,tabl

Author

R. H. Hardin, May 18 2018

Status

approved