A240649 T(n,k)=Number of nXk 0..1 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..1 introduced in row major order.

0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 6, 3, 3, 5, 6, 8, 8, 6, 5, 8, 10, 23, 18, 23, 10, 8, 13, 21, 60, 61, 61, 60, 21, 13, 21, 42, 149, 168, 232, 168, 149, 42, 21, 34, 86, 396, 526, 953, 953, 526, 396, 86, 34, 55, 179, 1050, 1643, 4343, 5304, 4343, 1643, 1050, 179, 55, 89, 370

Offset: 1

Author

R. H. Hardin, Apr 09 2014

Keywords

• nonn
• tabl

Comments

Table starts

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

..1...2....2.....3......6......10........21.........42..........86..........179

..1...2....6.....8.....23......60.......149........396........1050.........2814

..2...3....8....18.....61.....168.......526.......1643........5524........18762

..3...6...23....61....232.....953......4343......19458.......90165.......421048

..5..10...60...168....953....5304.....29481.....168320......990468......5920658

..8..21..149...526...4343...29481....227270....1748201....14230080....116070258

.13..42..396..1643..19458..168320...1748201...18030130...191002776...2052931147

.21..86.1050..5524..90165..990468..14230080..191002776..2764522654..39961388170

.34.179.2814.18762.421048.5920658.116070258.2052931147.39961388170.770199142784

Examples

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

Links

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

Crossrefs

Column 1 is A000045(n-1)

Column 2 is A240513(n-2)

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) -a(n-3) -2*a(n-4) +a(n-5)

k=3: [order 20]

k=4: [order 48]