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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.

%I A232275 #12 Jul 23 2025 07:14:06
%S A232275 1,2,2,4,24,4,8,48,48,8,14,96,72,96,14,26,192,120,120,192,26,48,384,
%T A232275 216,168,216,384,48,88,768,408,264,264,408,768,88,162,1536,792,456,
%U A232275 360,456,792,1536,162,298,3072,1560,840,552,552,840,1560,3072,298,548,6144,3096
%N 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.
%C A232275 Table starts
%C A232275 ...1....2....4....8...14...26...48...88..162...298...548..1008..1854...3410
%C A232275 ...2...24...48...96..192..384..768.1536.3072..6144.12288.24576.49152..98304
%C A232275 ...4...48...72..120..216..408..792.1560.3096..6168.12312.24600.49176..98328
%C A232275 ...8...96..120..168..264..456..840.1608.3144..6216.12360.24648.49224..98376
%C A232275 ..14..192..216..264..360..552..936.1704.3240..6312.12456.24744.49320..98472
%C A232275 ..26..384..408..456..552..744.1128.1896.3432..6504.12648.24936.49512..98664
%C A232275 ..48..768..792..840..936.1128.1512.2280.3816..6888.13032.25320.49896..99048
%C A232275 ..88.1536.1560.1608.1704.1896.2280.3048.4584..7656.13800.26088.50664..99816
%C A232275 .162.3072.3096.3144.3240.3432.3816.4584.6120..9192.15336.27624.52200.101352
%C A232275 .298.6144.6168.6216.6312.6504.6888.7656.9192.12264.18408.30696.55272.104424
%H A232275 R. H. Hardin, <a href="/A232275/b232275.txt">Table of n, a(n) for n = 1..924</a>
%F A232275 Empirical for column k:
%F A232275 k=1: a(n) = a(n-1) +a(n-2) +a(n-3) for n>4
%F A232275 k=2: a(n) = 2*a(n-1) for n>2
%F A232275 k=3: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A232275 k=4: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A232275 k=5: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A232275 k=6: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A232275 k=7: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A232275 Apparently T(n,k)=12*(2^(n-1)+2^(k-1)-2) for n>1 and k>1
%e A232275 Some solutions for n=7 k=4
%e A232275 ..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....0..2..0..2
%e A232275 ..1..2..1..2....3..2..3..2....3..2..3..2....0..1..0..1....3..1..3..1
%e A232275 ..0..3..0..3....1..0..1..0....1..0..1..0....3..2..3..2....0..2..0..2
%e A232275 ..1..2..1..2....3..2..3..2....2..3..2..3....1..0..1..0....3..1..3..1
%e A232275 ..3..0..3..0....0..1..0..1....1..0..1..0....3..2..3..2....2..0..2..0
%e A232275 ..2..1..2..1....2..3..2..3....2..3..2..3....1..0..1..0....3..1..3..1
%e A232275 ..0..3..0..3....1..0..1..0....1..0..1..0....2..3..2..3....0..2..0..2
%Y A232275 Column 1 is A135491(n-1)
%Y A232275 Column 2 is A003945(n+2)
%Y A232275 Diagonal is 12*A000918 for n>1
%K A232275 nonn,tabl
%O A232275 1,2
%A A232275 _R. H. Hardin_, Nov 22 2013