A253367 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 2X2 and 3X3 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally and vertically

152, 272, 272, 560, 424, 560, 976, 960, 960, 976, 1904, 1536, 2992, 1536, 1904, 3472, 3136, 5280, 5280, 3136, 3472, 6544, 5664, 13800, 8904, 13800, 5664, 6544, 12048, 10496, 27072, 23936, 23936, 27072, 10496, 12048, 22704, 20000, 63496, 53128, 76840

Offset

1,1

Comments

Table starts

...152...272....560.....976....1904.....3472......6544.....12048......22704

...272...424....960....1536....3136.....5664.....10496.....20000......36160

...560...960...2992....5280...13800....27072.....63496....130464.....297288

...976..1536...5280....8904...23936....53128....112864....286888.....563680

..1904..3136..13800...23936...76840...175328....438504...1151296....2656232

..3472..5664..27072...53128..175328...520888...1255456...4289736....9455136

..6544.10496..63496..112864..438504..1255456...3424264..12086016...30463848

.12048.20000.130464..286888.1151296..4289736..12086016..51091912..132958016

.22704.36160.297288..563680.2656232..9455136..30463848.132958016..419412744

.41680.68672.612480.1423176.7032608.31254904.105411360.528171592.1709806624

Links

R. H. Hardin, Table of n, a(n) for n = 1..1057

Formula

Empirical for column k:

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

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

k=3: a(n) = 7*a(n-2) -15*a(n-4) +17*a(n-6) +16*a(n-8) for n>11

k=4: [order 14] for n>16

k=5: [order 16] for n>19

k=6: [order 22] for n>26

k=7: [order 30] for n>33

Example

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

Crossrefs

Sequence in context: A234348 A185394 A097640 * A253360 A252363 A248816

Adjacent sequences: A253364 A253365 A253366 * A253368 A253369 A253370

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2014

Status

approved