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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
15
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 08 2013
STATUS
approved