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

1,5

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n-1)

Column 2 is A240513(n-2)

Sequence in context: A233296 A029228 A029215 * A226942 A030371 A029550

Adjacent sequences: A240646 A240647 A240648 * A240650 A240651 A240652

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 09 2014

Status

approved