A296541 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 16, 8, 1, 1, 15, 37, 37, 15, 1, 1, 26, 96, 126, 96, 26, 1, 1, 45, 254, 431, 431, 254, 45, 1, 1, 80, 654, 1554, 2104, 1554, 654, 80, 1, 1, 140, 1709, 5601, 10734, 10734, 5601, 1709, 140, 1, 1, 245, 4472, 20036, 53995, 78660, 53995, 20036

Offset: 1

Author

R. H. Hardin, Dec 15 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

.1...3....5.....8......15.......26........45..........80..........140

.1...5...16....37......96......254.......654........1709.........4472

.1...8...37...126.....431.....1554......5601.......20036........71722

.1..15...96...431....2104....10734.....53995......270584......1360373

.1..26..254..1554...10734....78660....560942.....3987615.....28515358

.1..45..654..5601...53995...560942...5705431....57470370....581613058

.1..80.1709.20036..270584..3987615..57470370...820373528..11761387456

.1.140.4472.71722.1360373.28515358.581613058.11761387456.239372827502

Examples

			Some solutions for n=6 k=4
..0..1..0..0. .0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..1..1..1
..0..1..1..0. .1..1..0..0. .0..0..0..0. .0..1..0..1. .0..1..1..0
..0..1..0..0. .1..0..0..1. .1..1..0..1. .0..1..1..0. .1..0..1..0
..1..1..1..0. .0..0..1..1. .1..0..1..1. .0..0..0..0. .1..0..1..0
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 2 is A193147(n+1).

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 39]