A230989 T(n,k)=Number of white square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero

1, 1, 1, 2, 1, 2, 3, 4, 4, 3, 5, 5, 11, 5, 5, 8, 15, 24, 24, 15, 8, 13, 20, 59, 47, 59, 20, 13, 21, 57, 139, 191, 191, 139, 57, 21, 34, 77, 332, 396, 685, 396, 332, 77, 34, 55, 218, 796, 1573, 2379, 2379, 1573, 796, 218, 55, 89, 295, 1903, 3317, 8357, 7357, 8357, 3317

Offset

1,4

Comments

Table starts

..1..1...2....3.....5......8......13......21.......34........55.........89

..1..1...4....5....15.....20......57......77......218.......295........835

..2..4..11...24....59....139.....332.....796.....1903......4563......10934

..3..5..24...47...191....396....1573....3317....13176.....27805.....110739

..5.15..59..191...685...2379....8357...29493...103842....366761....1295168

..8.20.139..396..2379...7357...43004..135154...793041...2491365...14671984

.13.57.332.1573..8357..43004..223270.1168723..6098749..31928221..167211867

.21.77.796.3317.29493.135154.1168723.5447557.47403200.220834521.1930022303

Links

R. H. Hardin, Table of n, a(n) for n = 1..684

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-2) -5*a(n-4) +2*a(n-6)

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

k=4: [order 18, even terms]

k=5: [order 32]

k=6: [order 70, even terms]

Example

Some solutions for n=6 k=4
..0..x..0..x..1....0..x..0..x..1....0..x..0..x..0....0..x..0..x..0
..x..1..x..0..x....x..1..x..0..x....x..1..x..1..x....x..1..x..1..x
..1..x..0..x..1....0..x..1..x..1....0..x..0..x..1....1..x..0..x..1
..x..0..x..1..x....x..0..x..1..x....x..1..x..0..x....x..0..x..0..x
..1..x..1..x..0....1..x..0..x..0....0..x..1..x..0....1..x..1..x..1
..x..0..x..0..x....x..0..x..1..x....x..0..x..1..x....x..0..x..0..x
..1..x..1..x..1....1..x..1..x..0....1..x..0..x..0....1..x..1..x..1

Crossrefs

Column 1 is A000045

Sequence in context: A295164 A241419 A203108 * A321392 A030339 A030383

Adjacent sequences: A230986 A230987 A230988 * A230990 A230991 A230992

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 02 2013

Status

approved