A251268 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having x11-x00 less than x10-x01.

11, 26, 35, 57, 114, 108, 120, 313, 480, 337, 247, 772, 1667, 2058, 1049, 502, 1775, 4930, 9109, 8812, 3268, 1013, 3894, 13052, 32636, 49872, 37772, 10179, 2036, 8277, 31936, 100843, 217634, 273607, 161906, 31707, 4083, 17224, 73805, 279718, 790734

Offset

1,1

Comments

Table starts

.....11.......26........57........120.........247..........502.........1013

.....35......114.......313........772........1775.........3894.........8277

....108......480......1667.......4930.......13052........31936........73805

....337.....2058......9109......32636......100843.......279718.......715685

...1049.....8812.....49872.....217634......790734......2510004......7189937

...3268....37772....273607....1457326.....6247708.....22806904.....73607411

..10179...161906...1501739....9772880....49523566....208452452....760734085

..31707...694042...8244503...65582500...393172015...1910905110...7901650053

..98764..2975162..45265163..440223510..3123669457..17543333688..82288916360

.307641.12753740.248529844.2955392154.24825649060.161181383956.858174176431

Links

R. H. Hardin, Table of n, a(n) for n = 1..479

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 16]

k=5: [order 36]

k=6: [order 62]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)

n=2: a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5)

n=3: [order 8]

n=4: [order 10]

n=5: [order 12]

n=6: [order 14]

n=7: [order 16]

Example

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

Crossrefs

Column 1 is A052550(n+2)

Row 1 is A000295(n+3)

Sequence in context: A137015 A260903 A316315 * A174223 A247466 A329809

Adjacent sequences: A251265 A251266 A251267 * A251269 A251270 A251271

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 01 2014

Status

approved