A238323 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors

3, 9, 9, 22, 67, 22, 51, 376, 376, 51, 121, 1867, 4294, 1867, 121, 292, 9489, 41046, 41046, 9489, 292, 704, 50232, 405636, 721939, 405636, 50232, 704, 1691, 267174, 4245918, 13265123, 13265123, 4245918, 267174, 1691, 4059, 1408341, 44773061

Offset

1,1

Comments

Table starts

....3.......9.........22............51.............121................292

....9......67........376..........1867............9489..............50232

...22.....376.......4294.........41046..........405636............4245918

...51....1867......41046........721939........13265123..........261676376

..121....9489.....405636......13265123.......459256128........17315827838

..292...50232....4245918.....261676376.....17315827838......1266938409578

..704..267174...44773061....5206684654....658399071392.....93481623913793

.1691.1408341..466364332..102053610873..24577532667851...6747651769489946

.4059.7395987.4831077908.1987295524193.910817281935043.483084194221969236

Links

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

Formula

Empirical for column k:

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

k=2: [order 13]

k=3: [order 43]

Example

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

Crossrefs

Column 1 is A202882(n+1)

Sequence in context: A224057 A224310 A224374 * A223742 A223725 A223831

Adjacent sequences: A238320 A238321 A238322 * A238324 A238325 A238326

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 24 2014

Status

approved