A240636 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..1 introduced in row major order

1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 81, 129, 81, 16, 32, 264, 637, 637, 264, 32, 64, 857, 3147, 4989, 3147, 857, 64, 128, 2785, 15590, 38634, 38634, 15590, 2785, 128, 256, 9050, 77269, 299329, 470170, 299329, 77269, 9050, 256, 512, 29407, 382933, 2319211

Offset

1,2

Comments

Table starts

...1.....2.......4..........8...........16.............32...............64

...2.....8......25.........81..........264............857.............2785

...4....25.....129........637.........3147..........15590............77269

...8....81.....637.......4989........38634.........299329..........2319211

..16...264....3147......38634.......470170........5723270.........69637692

..32...857...15590.....299329......5723270......109584463.......2097636322

..64..2785...77269....2319211.....69637692.....2097636322......63213422873

.128..9050..382933...17971509....847232955....40145256595....1904782876182

.256.29407.1897681..139264013..10307784448...768275538054...57392644533582

.512.95557.9404215.1079178635.125409399932.14702668840259.1729241310772922

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) +a(n-2) -2*a(n-4)

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

k=4: [order 32]

Example

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

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A240478

Sequence in context: A317604 A038208 A240484 * A281344 A298287 A299359

Adjacent sequences: A240633 A240634 A240635 * A240637 A240638 A240639

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 09 2014

Status

approved