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

Author

R. H. Hardin, Nov 22 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A135491(n-1)

Column 2 is A003945(n+2)

Diagonal is 12*A000918 for n>1

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