A253350 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal maximum minus antidiagonal maximum nondecreasing horizontally, vertically and ne-to-sw antidiagonally

16, 47, 47, 125, 173, 125, 335, 724, 735, 335, 907, 3160, 4800, 3192, 907, 2470, 13810, 31156, 30920, 13917, 2470, 6740, 60368, 200740, 305872, 199512, 60779, 6740, 18406, 263920, 1294016, 3006936, 3013228, 1285960, 265605, 18406, 50278, 1153880

Offset

1,1

Comments

Table starts

.....16.......47........125..........335............907.............2470

.....47......173........724.........3160..........13810............60368

....125......735.......4800........31156.........200740..........1294016

....335.....3192......30920.......305872........3006936.........29746140

....907....13917.....199512......3013228.......44555528........665370612

...2470....60779....1285960.....29779356......664592224......15101198444

...6740...265605....8289288....294392852.....9887498224.....340936886060

..18406..1161035...53433608...2912660356...147292687568....7720152604732

..50278..5075841..344449224..28819853684..2193102920288..174647893015868

.137354.22191959.2220470152.285212776212.32661849908016.3953303875494396

Links

R. H. Hardin, Table of n, a(n) for n = 1..361

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -2*a(n-3) for n>6

k=2: a(n) = 6*a(n-1) -5*a(n-2) -12*a(n-3) +12*a(n-4) for n>6

k=3: [order 7] for n>8

k=4: [order 11] for n>14

k=5: [order 23] for n>25

k=6: [order 43] for n>46

k=7: [order 84] for n>87

Empirical for row n:

n=1: a(n) = 3*a(n-1) -2*a(n-3) for n>6

n=2: a(n) = 5*a(n-1) -12*a(n-3) for n>6

n=3: [order 7] for n>10

n=4: [order 11] for n>15

n=5: [order 23] for n>26

n=6: [order 43] for n>47

n=7: [order 84] for n>88

Example

Some solutions for n=3 k=4
..1..0..0..1..1....0..1..0..0..0....0..1..1..1..1....1..1..1..1..1
..1..1..1..1..0....1..1..1..1..1....1..1..1..0..0....0..0..0..1..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..0
..0..0..0..1..0....0..0..1..0..1....0..0..0..0..0....0..0..1..1..0

Crossrefs

Column 1 and row 1 are A204609

Sequence in context: A126370 A133345 A253231 * A204616 A204800 A194268

Adjacent sequences: A253347 A253348 A253349 * A253351 A253352 A253353

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2014

Status

approved