A235449 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise

16, 58, 58, 208, 382, 208, 742, 2476, 2476, 742, 2644, 15936, 28962, 15936, 2644, 9418, 102376, 335898, 335898, 102376, 9418, 33544, 657290, 3886120, 7017768, 3886120, 657290, 33544, 119470, 4219322, 44920240, 146213244, 146213244, 44920240

Offset

1,1

Comments

Table starts

......16.........58..........208.............742...............2644

......58........382.........2476...........15936.............102376

.....208.......2476........28962..........335898............3886120

.....742......15936.......335898.........7017768..........146213244

....2644.....102376......3886120.......146213244.........5485253042

....9418.....657290.....44920240......3043145826.......205551169550

...33544....4219322....519099694.....63315473350......7699719982722

..119470...27083638...5998218844...1317184566572....288383414393138

..425500..173846264..69307887110..27401048899854..10800536489561114

.1515442.1115891712.800828757910.570010121664030.404495358726610494

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -8*a(n-2) -16*a(n-3) +12*a(n-4) +14*a(n-5) -a(n-6) -2*a(n-7)

k=3: [order 19]

k=4: [order 53]

Example

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

Crossrefs

Column 1 is A180143(n+1)

Sequence in context: A316443 A223313 A235679 * A235736 A235517 A253428

Adjacent sequences: A235446 A235447 A235448 * A235450 A235451 A235452

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2014

Status

approved