A235893 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock

40, 112, 112, 352, 232, 352, 1216, 568, 568, 1216, 4480, 1624, 1096, 1624, 4480, 17152, 5272, 2536, 2536, 5272, 17152, 67072, 18712, 6952, 4744, 6952, 18712, 67072, 265216, 70168, 21928, 10696, 10696, 21928, 70168, 265216, 1054720, 271384, 76456, 28744

Offset

1,1

Comments

Table starts

......40.....112.....352....1216....4480...17152...67072..265216..1054720

.....112.....232.....568....1624....5272...18712...70168..271384..1067032

.....352.....568....1096....2536....6952...21928...76456..283816..1091752

....1216....1624....2536....4744...10696...28744...89416..309064..1141576

....4480....5272....6952...10696...19720...43912..116872..361096..1242760

...17152...18712...21928...28744...43912...80392..177928..471304..1451272

...67072...70168...76456...89416..116872..177928..324616..716296..1892872

..265216..271384..283816..309064..361096..471304..716296.1304584..2874376

.1054720.1067032.1091752.1141576.1242760.1451272.1892872.2874376..5230600

.4206592.4231192.4280488.4379464.4578952.4984072.5818888.7586824.11515912

Links

R. H. Hardin, Table of n, a(n) for n = 1..309

Formula

Empirical for diagonal and column k (the k=2..7 recurrence also works for k=1; apparently all rows and columns satisfy the same order 3 recurrence):

diagonal: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

k=1: a(n) = 6*a(n-1) -8*a(n-2)

k=2..7..(?): a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

Example

Some solutions for n=4 k=4
..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
..1..3..1..3..1....1..1..1..2..2....3..1..3..1..3....0..3..0..2..3
..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
..1..3..1..3..1....1..1..1..2..2....1..3..1..3..1....0..3..0..2..3
..1..3..1..3..1....2..2..2..1..1....3..1..3..1..3....0..3..0..2..3

Crossrefs

Sequence in context: A123992 A235301 A235291 * A192791 A345970 A235886

Adjacent sequences: A235890 A235891 A235892 * A235894 A235895 A235896

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2014

Status

approved