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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
14
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 30 2014
STATUS
approved