A232275 T(n,k)=Number of nXk 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, vertically, diagonally or antidiagonally, and no adjacent values equal.

1, 2, 2, 4, 24, 4, 8, 48, 48, 8, 14, 96, 72, 96, 14, 26, 192, 120, 120, 192, 26, 48, 384, 216, 168, 216, 384, 48, 88, 768, 408, 264, 264, 408, 768, 88, 162, 1536, 792, 456, 360, 456, 792, 1536, 162, 298, 3072, 1560, 840, 552, 552, 840, 1560, 3072, 298, 548, 6144, 3096

Offset

1,2

Comments

Table starts

...1....2....4....8...14...26...48...88..162...298...548..1008..1854...3410

...2...24...48...96..192..384..768.1536.3072..6144.12288.24576.49152..98304

...4...48...72..120..216..408..792.1560.3096..6168.12312.24600.49176..98328

...8...96..120..168..264..456..840.1608.3144..6216.12360.24648.49224..98376

..14..192..216..264..360..552..936.1704.3240..6312.12456.24744.49320..98472

..26..384..408..456..552..744.1128.1896.3432..6504.12648.24936.49512..98664

..48..768..792..840..936.1128.1512.2280.3816..6888.13032.25320.49896..99048

..88.1536.1560.1608.1704.1896.2280.3048.4584..7656.13800.26088.50664..99816

.162.3072.3096.3144.3240.3432.3816.4584.6120..9192.15336.27624.52200.101352

.298.6144.6168.6216.6312.6504.6888.7656.9192.12264.18408.30696.55272.104424

Links

R. H. Hardin, Table of n, a(n) for n = 1..924

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) for n>2

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

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

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

k=6: a(n) = 3*a(n-1) -2*a(n-2) for n>3

k=7: a(n) = 3*a(n-1) -2*a(n-2) for n>3

Apparently T(n,k)=12*(2^(n-1)+2^(k-1)-2) for n>1 and k>1

Example

Some solutions for n=7 k=4
..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....0..2..0..2
..1..2..1..2....3..2..3..2....3..2..3..2....0..1..0..1....3..1..3..1
..0..3..0..3....1..0..1..0....1..0..1..0....3..2..3..2....0..2..0..2
..1..2..1..2....3..2..3..2....2..3..2..3....1..0..1..0....3..1..3..1
..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....2..0..2..0
..2..1..2..1....2..3..2..3....2..3..2..3....1..0..1..0....3..1..3..1
..0..3..0..3....1..0..1..0....1..0..1..0....2..3..2..3....0..2..0..2

Crossrefs

Column 1 is A135491(n-1)

Column 2 is A003945(n+2)

Diagonal is 12*A000918 for n>1

Sequence in context: A287909 A263439 A270527 * A257612 A387762 A009541

Adjacent sequences: A232272 A232273 A232274 * A232276 A232277 A232278

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2013

Status

approved