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A231463
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
12
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Column 1 is A231337
Sequence in context: A365724 A112305 A231396 * A218616 A323173 A324184
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 09 2013
STATUS
approved