A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 3, 3, 3, 3, 0, 0, 2, 3, 3, 3, 2, 0, 0, 6, 8, 4, 4, 8, 6, 0, 0, 6, 16, 22, 32, 22, 16, 6, 0, 0, 11, 32, 39, 92, 92, 39, 32, 11, 0, 0, 16, 70, 102, 270, 366, 270, 102, 70, 16, 0, 0, 22, 135, 298, 1262, 1592, 1592, 1262, 298, 135, 22, 0, 0, 37, 293

Offset: 1

Author

R. H. Hardin, Mar 04 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

.0..1..1...1....3.....2......6.......6.......11........16..........22

.0..1..0...3....3.....8.....16......32.......70.......135.........293

.0..1..3...3....4....22.....39.....102......298.......833........2105

.0..3..3...4...32....92....270....1262.....3561.....13976.......48859

.0..2..8..22...92...366...1592....6925....36101....161645......762469

.0..6.16..39..270..1592..12042...75739...490425...3084820....19634393

.0..6.32.102.1262..6925..75739..729062..5841423..53750463...469053654

.0.11.70.298.3561.36101.490425.5841423.70536528.833035233.10021999204

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..263

Crossrefs

Column 2 is A062200(n-2).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-4)

k=3: [order 14]

k=4: [order 43] for n>45