A231070 T(n,k)=Number of black 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, 3, 2, 3, 4, 4, 3, 5, 11, 11, 11, 5, 8, 15, 24, 24, 15, 8, 13, 42, 59, 89, 59, 42, 13, 21, 57, 139, 191, 191, 139, 57, 21, 34, 161, 332, 748, 685, 748, 332, 161, 34, 55, 218, 796, 1573, 2379, 2379, 1573, 796, 218, 55, 89, 617, 1903, 6259, 8357, 13785, 8357

Offset

1,4

Comments

Table starts

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

..1...3...4...11....15.....42......57......161......218.......617........835

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

..3..11..24...89...191....748....1573.....6259....13176.....52497.....110739

..5..15..59..191...685...2379....8357....29493...103842....366761....1295168

..8..42.139..748..2379..13785...43004...253150...793041...4669709...14671984

.13..57.332.1573..8357..43004..223270..1168723..6098749..31928221..167211867

.21.161.796.6259.29493.253150.1168723.10204445.47403200.414060681.1930022303

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=4 k=4
..x..0..x..1..x....x..0..x..0..x....x..0..x..1..x....x..0..x..0..x
..1..x..0..x..0....1..x..1..x..1....1..x..0..x..1....0..x..1..x..0
..x..1..x..0..x....x..0..x..0..x....x..1..x..0..x....x..1..x..1..x
..0..x..1..x..1....1..x..1..x..1....0..x..0..x..1....1..x..0..x..1
..x..1..x..0..x....x..0..x..0..x....x..1..x..1..x....x..0..x..0..x

Crossrefs

Column 1 is A000045

Column 3 is A230984

Column 5 is A230986

Column 7 is A230988

Sequence in context: A129600 A355663 A081388 * A230252 A295424 A002372

Adjacent sequences: A231067 A231068 A231069 * A231071 A231072 A231073

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved