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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 04:53 EDT 2021. Contains 347703 sequences. (Running on oeis4.)