A231523 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

2, 2, 4, 4, 10, 8, 7, 34, 21, 16, 12, 107, 153, 48, 32, 21, 342, 865, 776, 113, 64, 37, 1069, 4665, 7697, 3861, 261, 128, 65, 3381, 25556, 70462, 66499, 18721, 601, 256, 114, 10689, 144847, 680302, 1031105, 571226, 91993, 1390, 512, 200, 33808, 817539

Offset: 1

Author

R. H. Hardin, Nov 10 2013

Keywords

• nonn
• tabl

Comments

Table starts

....2....2........4..........7...........12..............21................37

....4...10.......34........107..........342............1069..............3381

....8...21......153........865.........4665...........25556............144847

...16...48......776.......7697........70462..........680302...........6935963

...32..113.....3861......66499......1031105........17572772.........322599407

...64..261....18721.....571226.....15000701.......451200772.......14940780666

..128..601....91993....4944075....219937967.....11683058939......697702378939

..256.1390...453274...42759650...3222629836....302190345444....32529760276112

..512.3216..2223662..369356733..47159743290...7806399525348..1514885617016157

.1024.7435.10915727.3191749214.690399979855.201765495180944.70592106166184098

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A000079

Column 2 is A231376

Row 1 is A005251(n+2)

Formula

Empirical for column k:

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

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

k=3: [order 13] for n>14

k=4: [order 24] for n>25

k=5: [order 70] for n>71

Empirical for row n:

n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4

n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)

n=3: [order 16] for n>17

n=4: [order 39] for n>40