A232406 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or vertically, with no adjacent elements equal

4, 4, 4, 8, 16, 8, 16, 20, 20, 16, 28, 72, 52, 72, 28, 52, 124, 176, 176, 124, 52, 96, 356, 484, 1120, 484, 356, 96, 176, 664, 1500, 2788, 2788, 1500, 664, 176, 324, 1808, 4416, 16884, 13532, 16884, 4416, 1808, 324, 596, 3572, 13220, 44528, 71888, 71888, 44528

Offset

1,1

Comments

Table starts

...4....4......8......16.......28.........52..........96..........176

...4...16.....20......72......124........356.........664.........1808

...8...20.....52.....176......484.......1500........4416........13220

..16...72....176....1120.....2788......16884.......44528.......255432

..28..124....484....2788....13532......71888......370876......1936620

..52..356...1500...16884....71888.....798692.....3508240.....38129964

..96..664...4416...44528...370876....3508240....31802528....296151320

.176.1808..13220..255432..1936620...38129964...296151320...5824262024

.324.3572..39524..706796.10086748..171206912..2734362948..45696457832

.596.9148.117892.3869856.52577472.1824149740.25388000332.894239301036

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: [order 9]

k=3: [order 12]

k=4: [order 29]

k=5: [order 56]

Example

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

Crossrefs

Column 1 is 4*A000073(n+1)

Sequence in context: A110757 A167184 A276113 * A322040 A085071 A341324

Adjacent sequences: A232403 A232404 A232405 * A232407 A232408 A232409

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 23 2013

Status

approved