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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 16
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 25 2013
STATUS
approved

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Last modified July 21 09:38 EDT 2024. Contains 374472 sequences. (Running on oeis4.)