A303325 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 8, 1, 8, 1, 8, 4, 2, 16, 1, 32, 1, 8, 1, 32, 1, 32, 4, 2, 16, 2, 64, 1, 128, 1, 12, 4, 32, 1, 128, 1, 128, 4, 10, 64, 3, 64, 2, 256, 1, 512, 1, 46, 25, 62, 3, 128, 1, 512, 1, 512, 4, 50, 368, 56, 204, 10, 256, 2, 1024, 1, 2048, 1, 204, 201, 758, 136, 744, 9, 512, 1

Offset: 1

Author

R. H. Hardin, Apr 21 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1.1...1..1...1....1.....1.....1.......1........1.........1..........1

...2.2...8..8..32...32...128...128.....512......512......2048.......2048

...4.1...4..1...4....1.....4.....1.......4........1.........4..........1

...8.2...8..2..12...10....46....50.....204......290......1034.......1682

..16.1..16..4..64...25...368...201....2545.....1855.....21082......17922

..32.2..32..3..62...56...758...822...11950....15100....206189.....274746

..64.1..64..3.204..136..2956..3929...69328...130531...2005898....4227664

.128.2.128.10.744..531.15494.24759..629227..1489177..33766564...89782726

.256.1.256..9.900.1035.44101.97205.3531980.11297739.359263250.1265799068

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..242

Crossrefs

Column 1 is A000079(n-1).

Column 3 is A000079(n-1) for n>2.

Row 2 is A158302(n+1).

Row 3 is A010685(n+8).

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) for n>3

k=4: [order 55] for n>57

k=5: [order 33] for n>35

Empirical for row n:

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

n=2: a(n) = 4*a(n-2)

n=3: a(n) = a(n-2)

n=4: [order 18] for n>19

n=5: [order 34] for n>35