A232515 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, diagonally or antidiagonally, with no adjacent elements equal

4, 16, 4, 16, 52, 8, 54, 32, 200, 16, 74, 326, 128, 784, 28, 218, 250, 2516, 400, 3052, 52, 340, 2138, 1730, 19138, 1344, 11900, 96, 868, 1956, 32084, 10118, 145682, 4416, 46432, 176, 1494, 13976, 24388, 475086, 64290, 1110752, 14608, 181184, 324, 3528

Offset

1,1

Comments

Table starts

...4......16.....16.........54........74...........218..........340

...4......52.....32........326.......250..........2138.........1956

...8.....200....128.......2516......1730.........32084........24388

..16.....784....400......19138.....10118........475086.......270400

..28....3052...1344.....145682.....64290.......7059918......3267824

..52...11900...4416....1110752....399122.....105188684.....38988416

..96...46432..14608....8470018...2523098....1567758430....476578496

.176..181184..48224...64594290..15907690...23370338858...5831607392

.324..707044.159296..492627324.100603770..348398002228..71731172848

.596.2759212.526096.3757052022.636270550.5193906376594.883465590796

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

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

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

k=4: [order 14]

k=5: [order 18] for n>19

k=6: [order 49]

k=7: [order 78]

Empirical for row n:

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

n=2: a(n) = 6*a(n-2) +a(n-3) +3*a(n-4) +a(n-5) -2*a(n-6) -2*a(n-7)

n=3: [order 9]

n=4: [order 23]

n=5: [order 42]

n=6: [order 90]

Example

Some solutions for n=5 k=4
..0..1..2..1..0....0..1..2..1..2....0..1..0..1..0....2..1..0..1..0
..0..1..2..1..0....0..1..2..1..0....2..1..2..1..0....2..1..2..1..2
..2..1..2..1..0....0..1..0..1..2....2..1..0..1..0....2..1..2..1..2
..2..1..0..1..2....0..1..0..1..0....2..1..2..1..2....2..1..0..1..0
..2..1..2..1..2....0..1..2..1..0....2..1..2..1..0....2..1..0..1..2
..0..1..0..1..0....2..1..0..1..0....0..1..2..1..2....0..1..0..1..2

Crossrefs

Sequence in context: A305833 A110650 A334840 * A010295 A059152 A059156

Adjacent sequences: A232512 A232513 A232514 * A232516 A232517 A232518

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 25 2013

Status

approved