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

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

R. H. Hardin, Table of n, a(n) for n = 1..97

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 * A379676 A218616 A323173

Adjacent sequences: A231460 A231461 A231462 * A231464 A231465 A231466

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 09 2013

Status

approved