A302381 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 76, 34, 0, 5, 161, 430, 475, 111, 0, 8, 601, 2886, 4640, 2771, 361, 0, 13, 2208, 19215, 56541, 48980, 16451, 1172, 0, 21, 8053, 127535, 688999, 1089035, 514655, 97160, 3809, 0, 34, 29415, 847604, 8334338, 24209608, 20993054

Offset: 1

Author

R. H. Hardin, Apr 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0.....1.......1.........2............3..............5................8

.0.....3......15........46..........161............601.............2208

.0....11......76.......430.........2886..........19215...........127535

.0....34.....475......4640........56541.........688999..........8334338

.0...111....2771.....48980......1089035.......24209608........535192095

.0...361...16451....514655.....20993054......849467774......34271733937

.0..1172...97160...5421003....404225195....29810775827....2195619257236

.0..3809..574671..57068484...7787623959..1046322460741..140685735128595

.0.12377.3397622.600825641.150008013842.36721875744312.9013655138528774

Examples

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

Links

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A232077(n-1).

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-4)

k=3: [order 11]

k=4: [order 26]

k=5: [order 84] for n>86

Empirical for row n:

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

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

n=3: [order 14] for n>15

n=4: [order 42] for n>43