A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 5, 13, 0, 5, 18, 26, 15, 34, 0, 8, 50, 84, 74, 48, 89, 0, 13, 128, 309, 468, 200, 155, 233, 0, 21, 338, 1108, 2036, 2856, 530, 499, 610, 0, 34, 882, 3979, 10982, 14016, 17800, 1394, 1602, 1597, 0, 55, 2312, 14314, 53440, 122232

Offset: 1

Author

R. H. Hardin, Mar 30 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0....1....1....2.......3........5..........8..........13............21

.0....2....2....8......18.......50........128.........338...........882

.0....5....5...26......84......309.......1108........3979.........14314

.0...13...15...74.....468.....2036......10982.......53440........271596

.0...34...48..200....2856....14016.....122232......813704.......6066698

.0...89..155..530...17800...100176....1366374....12824770.....133115004

.0..233..499.1394..110036...729297...15243860...204666568....2933712940

.0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404

.0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108

Examples

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

Links

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

Crossrefs

Column 2 is A001519.

Row 1 is A000045(n-1).

Row 2 is A175395(n-1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3)

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

k=5: [order 11] for n>12

k=6: [order 32] for n>33

k=7: [order 52] for n>54

Empirical for row n:

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

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

n=3: [order 20]