A251037 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction

110, 711, 636, 4050, 6089, 3550, 21720, 45560, 45150, 19112, 110852, 308423, 422538, 304421, 100633, 546600, 1907070, 3433899, 3396593, 1946207, 521227, 2624313, 11102613, 24844850, 32439684, 25346175, 12029009, 2668193, 12343573, 61631550

Offset

1,1

Comments

Table starts

......110........711........4050........21720.........110852..........546600

......636.......6089.......45560.......308423........1907070........11102613

.....3550......45150......422538......3433899.......24844850.......165531421

....19112.....304421.....3396593.....32439684......267606254......2010619868

...100633....1946207....25346175....279055227.....2592092409.....21672923484

...521227...12029009...179902335...2247957615....23202398270....213854374926

..2668193...72779934..1238480366..17355955112...197532441119...1992180311388

.13542602..434254685..8354406377.130154155397..1622322952743..17797755625080

.68311293.2567561554.55641391371.957718964643.13015173261675.154590936970044

Links

R. H. Hardin, Table of n, a(n) for n = 1..128

Formula

Empirical for column k:

k=1: [linear recurrence of order 12]

k=2: [order 28]

k=3: [order 59] for n>60

Empirical for row n:

n=1: [linear recurrence of order 13]

n=2: [order 32]

n=3: [order 60]

n=4: [order 98] for n>100

Example

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

Crossrefs

Sequence in context: A156852 A250536 A250529 * A251038 A074240 A283084

Adjacent sequences: A251034 A251035 A251036 * A251038 A251039 A251040

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved