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

1,5

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

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-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

Example

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A232077(n-1).

Sequence in context: A302472 A303254 A256068 * A303102 A302953 A350464

Adjacent sequences: A302378 A302379 A302380 * A302382 A302383 A302384

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 06 2018

Status

approved