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

Author

R. H. Hardin, Nov 15 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302

Column 2 is A231741

Row 1 is A203094 for n>1

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]