A232275 - OEIS

%I #10 Jan 03 2014 07:43:13

%S 1,2,2,4,24,4,8,48,48,8,14,96,72,96,14,26,192,120,120,192,26,48,384,

%T 216,168,216,384,48,88,768,408,264,264,408,768,88,162,1536,792,456,

%U 360,456,792,1536,162,298,3072,1560,840,552,552,840,1560,3072,298,548,6144,3096

%N 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

%C Table starts

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

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

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

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

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

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

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

%C ..88.1536.1560.1608.1704.1896.2280.3048.4584..7656.13800.26088.50664..99816

%C .162.3072.3096.3144.3240.3432.3816.4584.6120..9192.15336.27624.52200.101352

%C .298.6144.6168.6216.6312.6504.6888.7656.9192.12264.18408.30696.55272.104424

%H R. H. Hardin, <a href="/A232275/b232275.txt">Table of n, a(n) for n = 1..924</a>

%F Empirical for column k:

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

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

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

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

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

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

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

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

%e Some solutions for n=7 k=4

%e ..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....0..2..0..2

%e ..1..2..1..2....3..2..3..2....3..2..3..2....0..1..0..1....3..1..3..1

%e ..0..3..0..3....1..0..1..0....1..0..1..0....3..2..3..2....0..2..0..2

%e ..1..2..1..2....3..2..3..2....2..3..2..3....1..0..1..0....3..1..3..1

%e ..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....2..0..2..0

%e ..2..1..2..1....2..3..2..3....2..3..2..3....1..0..1..0....3..1..3..1

%e ..0..3..0..3....1..0..1..0....1..0..1..0....2..3..2..3....0..2..0..2

%Y Column 1 is A135491(n-1)

%Y Column 2 is A003945(n+2)

%Y Diagonal is 12*A000918 for n>1

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 22 2013