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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

%I

%S 4,16,4,16,52,8,54,32,200,16,74,326,128,784,28,218,250,2516,400,3052,

%T 52,340,2138,1730,19138,1344,11900,96,868,1956,32084,10118,145682,

%U 4416,46432,176,1494,13976,24388,475086,64290,1110752,14608,181184,324,3528

%N 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

%C Table starts

%C ...4......16.....16.........54........74...........218..........340

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

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

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

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

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

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

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

%C .324..707044.159296..492627324.100603770..348398002228..71731172848

%C .596.2759212.526096.3757052022.636270550.5193906376594.883465590796

%H R. H. Hardin, <a href="/A232515/b232515.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

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

%F 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)

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

%F k=4: [order 14]

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

%F k=6: [order 49]

%F k=7: [order 78]

%F Empirical for row n:

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

%F 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)

%F n=3: [order 9]

%F n=4: [order 23]

%F n=5: [order 42]

%F n=6: [order 90]

%e Some solutions for n=5 k=4

%e ..0..1..2..1..0....0..1..2..1..2....0..1..0..1..0....2..1..0..1..0

%e ..0..1..2..1..0....0..1..2..1..0....2..1..2..1..0....2..1..2..1..2

%e ..2..1..2..1..0....0..1..0..1..2....2..1..0..1..0....2..1..2..1..2

%e ..2..1..0..1..2....0..1..0..1..0....2..1..2..1..2....2..1..0..1..0

%e ..2..1..2..1..2....0..1..2..1..0....2..1..2..1..0....2..1..0..1..2

%e ..0..1..0..1..0....2..1..0..1..0....0..1..2..1..2....0..1..0..1..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 25 2013

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Last modified October 15 18:54 EDT 2021. Contains 348034 sequences. (Running on oeis4.)