A302728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 22, 23, 0, 5, 27, 29, 83, 61, 0, 8, 45, 74, 89, 301, 162, 0, 13, 98, 162, 287, 353, 1079, 421, 0, 21, 193, 363, 689, 1307, 941, 4064, 1103, 0, 34, 379, 782, 1723, 4505, 4491, 3316, 15183, 2890, 0, 55, 778, 1766, 4491, 16265, 20842, 17828

Offset: 1

Author

R. H. Hardin, Apr 12 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0....1.....1.....2......3.......5........8........13........21.........34

.0....3.....7....10.....27......45.......98.......193.......379........778

.0...10....22....29.....74.....162......363.......782......1766.......3953

.0...23....83....89....287.....689.....1723......4491.....10433......28009

.0...61...301...353...1307....4505....16265.....46773....136935.....481479

.0..162..1079...941...4491...20842....89121....286746...1022779....4520360

.0..421..4064..3316..17828..104969...532511...1932168...7608792...40495097

.0.1103.15183.12016..80293..623549..4281120..17200486..81226394..547173278

.0.2890.55012.34060.304958.3195095.26823700.120221024.683140749.5901256655

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 2 is A185828.

Column 4 is A302274.

Row 1 is A000045(n-1).

Row 2 is A302279.

Row 3 is A302280.

Formula

Empirical for column k:

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

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

k=3: [order 16]

k=4: [order 72] for n>73

Empirical for row n:

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

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

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

n=4: [order 68] for n>69