A231396 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order

3, 7, 4, 14, 8, 7, 33, 38, 15, 12, 78, 90, 100, 20, 23, 189, 363, 311, 272, 31, 44, 482, 1163, 1706, 1096, 740, 52, 87, 1225, 3985, 7844, 8340, 4085, 2061, 95, 172, 3238, 14650, 35696, 55788, 41237, 15732, 5834, 180, 343, 8565, 50088, 184692, 345022, 401240

Offset

1,1

Comments

Table starts

...3...7.....14......33........78........189........482.......1225.......3238

...4...8.....38......90.......363.......1163.......3985......14650......50088

...7..15....100.....311......1706.......7844......35696.....184692.....873979

..12..20....272....1096......8340......55788.....345022....2502891...16525492

..23..31....740....4085.....41237.....401240....3407422...34218952..319475231

..44..52...2061...15732....217846....3002376...35510853..491895476.6459555901

..87..95...5834...62039...1158551...22654165..374180527.7170248270

.172.180..16521..245850...6261166..172363558.3979476204

.343.351..46969..980361..34110556.1318257485

.684.692.133864.3915982.186830745

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)

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

k=3: [order 18]

k=4: [order 28] for n>31

Empirical for row n:

n=1: a(n) = 4*a(n-1) +a(n-2) -16*a(n-3) +4*a(n-4) +24*a(n-5) -16*a(n-6)

n=2: [order 21]

n=3: [order 83]

Example

Some solutions for n=4 k=4
..0..0..0..0..0....0..0..1..1..1....0..0..1..1..1....0..1..1..1..1
..1..1..0..0..0....1..1..0..0..0....0..1..0..1..1....1..0..0..0..0
..1..1..1..0..0....1..1..1..0..0....1..0..1..0..0....1..1..0..0..0
..1..1..0..0..0....1..1..0..0..0....1..1..0..0..0....1..1..1..2..2
..1..1..1..0..0....0..0..0..0..0....1..1..1..1..1....1..1..2..2..2

Crossrefs

Column 1 is A023105(n+2)

Sequence in context: A355927 A365724 A112305 * A231463 A218616 A323173

Adjacent sequences: A231393 A231394 A231395 * A231397 A231398 A231399

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 08 2013

Status

approved