A301669 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 23, 30, 23, 3, 5, 61, 118, 118, 61, 5, 8, 162, 407, 564, 407, 162, 8, 13, 421, 1498, 2793, 2793, 1498, 421, 13, 21, 1103, 5289, 14394, 21224, 14394, 5289, 1103, 21, 34, 2890, 19184, 71564, 146841, 146841, 71564, 19184, 2890, 34, 55

Offset: 1

Author

R. H. Hardin, Mar 25 2018

Keywords

• nonn
• tabl

Comments

Table starts

..0....1.....1.......2........3..........5...........8............13

..1....3....10......23.......61........162.........421..........1103

..1...10....30.....118......407.......1498........5289.........19184

..2...23...118.....564.....2793......14394.......71564........359659

..3...61...407....2793....21224.....146841.....1073621.......7703565

..5..162..1498...14394...146841....1537496....15498505.....159497778

..8..421..5289...71564..1073621...15498505...225780260....3307561389

.13.1103.19184..359659..7703565..159497778..3307561389...68862687289

.21.2890.68832.1808256.55506215.1631501428.48158543096.1434208027966

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..197

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A185828.

Formula

Empirical for column k:

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

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

k=3: [order 20]

k=4: [order 70]