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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A231376

Row 1 is A005251(n+2)

Sequence in context: A109525 A243330 A318838 * A114338 A170831 A133406

Adjacent sequences: A231520 A231521 A231522 * A231524 A231525 A231526

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 10 2013

Status

approved