A231940 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors

4, 4, 16, 16, 84, 64, 50, 668, 318, 256, 144, 5070, 8426, 1328, 1024, 422, 42104, 206808, 152180, 6064, 4096, 1268, 326010, 4736026, 11159202, 2462572, 26918, 16384, 3823, 2511252, 94464137, 691418144, 518972238, 36885538, 116909, 65536, 11472

Offset

1,1

Comments

Table starts

.......4.......4............16...............50................144

......16......84...........668.............5070..............42104

......64.....318..........8426...........206808............4736026

.....256....1328........152180.........11159202..........691418144

....1024....6064.......2462572........518972238........86074040354

....4096...26918......36885538......23280281589.....10417626293694

...16384..116909.....586971925....1098832065447...1320620287047433

...65536..511264....9394148948...52087504055935.167980047970274816

..262144.2248196..147360195020.2432351670277323

.1048576.9868600.2323912599668

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: [order 19] for n>20

k=3: [order 65] for n>66

Empirical for row n:

n=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8

n=2: [order 15]

Example

Some solutions for n=3 k=4
..0..0..0..1....0..0..0..3....2..0..0..2....0..2..2..1....0..0..1..0
..2..0..2..2....3..0..0..3....3..3..0..0....3..0..0..2....2..0..0..3
..2..3..0..0....1..2..3..0....1..0..0..2....2..0..0..0....0..2..3..2

Crossrefs

Column 1 is A000302

Column 2 is A231741

Row 1 is A203094 for n>1

Sequence in context: A213173 A222956 A170833 * A129884 A137725 A240035

Adjacent sequences: A231937 A231938 A231939 * A231941 A231942 A231943

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2013

Status

approved