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A231463
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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order
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12
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3, 7, 4, 14, 8, 7, 33, 38, 15, 12, 78, 90, 100, 20, 24, 197, 363, 311, 272, 32, 48, 531, 1163, 1709, 1096, 741, 56, 103, 1471, 4151, 7973, 8426, 4138, 2093, 111, 222, 4350, 16054, 37494, 57426, 42229, 16384, 6036, 230, 493, 13011, 57977, 207123, 367803, 425678
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OFFSET
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1,1
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COMMENTS
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Table starts
....3....7.....14......33.......78.......197.......531......1471.......4350
....4....8.....38......90......363......1163......4151.....16054......57977
....7...15....100.....311.....1709......7973.....37494....207123....1039577
...12...20....272....1096.....8426.....57426....367803...2845485...20018093
...24...32....741....4138....42229....425678...3759661..40527272..407446601
...48...56...2093...16384...229889...3306466..41018349.609662051.8698312947
..103..111...6036...67189..1275119..26262415.459675854
..222..230..17569..280852..7279729.212142656
..493..501..51839.1195147.42382102
.1100.1108.154480.5145988
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)
k=2: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5) for n>7
k=3: [order 32]
k=4: [order 52] for n>55
Empirical for row n:
n=1: [order 10]
n=2: [order 41]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1..1....0..0..1..1..1....0..1..1..1..0....0..0..1..1..1
..0..0..0..1..1....0..0..0..1..1....0..0..1..0..1....0..0..0..1..1
..0..0..0..0..1....0..0..2..2..2....0..0..0..1..0....0..0..0..0..0
..1..1..1..1..0....2..2..2..2..2....1..1..1..0..0....2..2..0..0..0
..1..1..1..0..0....2..2..2..3..3....1..1..0..0..0....2..2..2..3..3
..1..1..0..0..0....3..3..3..3..3....0..0..1..1..1....2..2..3..3..3
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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