A296405 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 3 neighboring 1s.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 17, 24, 17, 1, 1, 46, 82, 82, 46, 1, 1, 114, 316, 444, 316, 114, 1, 1, 289, 1182, 2868, 2868, 1182, 289, 1, 1, 757, 4560, 17783, 35561, 17783, 4560, 757, 1, 1, 1964, 17508, 110554, 368770, 368770, 110554, 17508, 1964, 1, 1, 5118, 67310

Offset

1,5

Comments

Table starts

.1....1.....1.......1.........1...........1.............1...............1

.1....4.....8......17........46.........114...........289.............757

.1....8....24......82.......316........1182..........4560...........17508

.1...17....82.....444......2868.......17783........110554..........688248

.1...46...316....2868.....35561......368770.......3939121........42629909

.1..114..1182...17783....368770.....6200926.....107541673......1896487480

.1..289..4560..110554...3939121...107541673....3068113721.....90097748288

.1..757.17508..688248..42629909..1896487480...90097748288...4427644444522

.1.1964.67310.4288144.457078213.33169242951.2600708602697.211857339895816

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

k=2: [order 9]

k=3: [order 20]

k=4: [order 52]

Example

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

Crossrefs

Sequence in context: A319251 A100754 A332307 * A174035 A303888 A305281

Adjacent sequences: A296402 A296403 A296404 * A296406 A296407 A296408

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 11 2017

Status

approved