A296635 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.

2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 47, 71, 47, 13, 21, 116, 260, 260, 116, 21, 34, 286, 966, 1444, 966, 286, 34, 55, 705, 3581, 8042, 8042, 3581, 705, 55, 89, 1738, 13275, 44783, 67488, 44783, 13275, 1738, 89, 144, 4285, 49209, 249329, 565149, 565149, 249329

Offset

1,1

Comments

Table starts

..2....3......5.......8........13..........21...........34.............55

..3....8.....19......47.......116.........286..........705...........1738

..5...19.....71.....260.......966........3581........13275..........49209

..8...47....260....1444......8042.......44783.......249329........1388229

.13..116....966....8042.....67488......565149......4733229.......39643699

.21..286...3581...44783....565149.....7121315.....89713772.....1130293195

.34..705..13275..249329...4733229....89713772...1700240351....32223940011

.55.1738..49209.1388229..39643699..1130293195..32223940011...918770773688

.89.4285.182422.7729475.332039800.14240708558.610746699603.26197140564540

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 39]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A296329.

Sequence in context: A198335 A339050 A296335 * A295051 A295379 A295352

Adjacent sequences: A296632 A296633 A296634 * A296636 A296637 A296638

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2017

Status

approved