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