A302367 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 31, 3, 16, 1, 72, 20, 109, 6, 32, 1, 168, 154, 77, 397, 10, 64, 1, 496, 284, 918, 209, 1430, 21, 128, 1, 1296, 1109, 3125, 6580, 774, 5110, 42, 256, 1, 3616, 3472, 21831, 26458, 49293, 3143, 18395, 86, 512, 1, 9760, 12763, 125193

Offset: 1

Author

R. H. Hardin, Apr 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

...2..2....12....20.......72.......168.........496..........1296

...4..2....31....20......154.......284........1109..........3472

...8..3...109....77......918......3125.......21831........125193

..16..6...397...209.....6580.....26458......405340.......3462040

..32.10..1430...774....49293....330505.....9361759.....134269527

..64.21..5110..3143...367512...3858625...188443738....4558781926

.128.42.18395.13556..2856621..48375470..4174802035..169314399506

.256.86.66203.60280.22185382.608124211.91302504318.6186362081201

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 50] for n>53

Empirical for row n:

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

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

n=3: [order 16] for n>18

n=4: [order 63] for n>66