A303102 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 77, 34, 0, 5, 161, 431, 486, 111, 0, 8, 601, 2913, 4667, 2869, 361, 0, 13, 2208, 19393, 58160, 49534, 17229, 1172, 0, 21, 8053, 128921, 709333, 1138331, 523578, 102952, 3809, 0, 34, 29415, 857789, 8650205, 25372284, 22292709

Offset

1,5

Comments

Table starts

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

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

.0....11......77.......431.........2913..........19393............128921

.0....34.....486......4667........58160.........709333...........8650205

.0...111....2869.....49534......1138331.......25372284.........568099880

.0...361...17229....523578.....22292709......906385523.......37220475492

.0..1172..102952...5550469....436394066....32409609245.....2441756629583

.0..3809..616065..58797885...8545589681..1158734336743...160164698180399

.0.12377.3685099.622939052.167325743073.41428642572259.10505922762123798

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 90] for n>91

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..1..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..1..0..1
..1..0..1..0. .1..1..1..1. .1..1..0..0. .0..1..1..1. .0..0..1..0
..1..0..0..1. .0..0..0..1. .1..1..1..1. .0..0..1..0. .1..0..0..0
..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..1..0..1. .0..1..1..1
..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..0..1..0. .1..0..0..0

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A232077(n-1).

Sequence in context: A303254 A256068 A302381 * A302953 A350464 A247706

Adjacent sequences: A303099 A303100 A303101 * A303103 A303104 A303105

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 18 2018

Status

approved