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A232589 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 antidiagonally, with no adjacent elements equal 16

%I

%S 0,10,2,2,34,4,26,12,124,6,20,152,42,456,10,70,108,996,122,1686,18,90,

%T 690,606,6406,332,6232,32,210,744,8104,3002,41328,882,23034,56,336,

%U 3232,7568,93236,14398,266490,2322,85130,98,674,4516,66744,68072,1079300

%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 or antidiagonally, with no adjacent elements equal

%C Table starts

%C ...0......10.....2........26.......20...........70..........90.............210

%C ...2......34....12.......152......108..........690.........744............3232

%C ...4.....124....42.......996......606.........8104........7568...........66744

%C ...6.....456...122......6406.....3002........93236.......68072.........1364998

%C ..10....1686...332.....41328....14398......1079300......595304........28339640

%C ..18....6232...882....266490....66950.....12486510.....5045772.......589476500

%C ..32...23034..2322...1718514...306022....144506106....41969054.....12273587770

%C ..56...85130..6092..11082034..1382638...1672314806...344123498....255585490674

%C ..98..314626.15962..71463916..6200520..19353375198..2791211292...5322596390316

%C .172.1162804.41802.460844060.27671244.223972627480.22459482618.110844512072980

%H R. H. Hardin, <a href="/A232589/b232589.txt">Table of n, a(n) for n = 1..477</a>

%F Empirical for column k:

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

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

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

%F k=4: a(n) = 5*a(n-1) +9*a(n-2) +2*a(n-3) +a(n-4) +2*a(n-5)

%F k=5: [order 14]

%F k=6: [order 23] for n>27

%F k=7: [order 44] for n>45

%F Empirical for row n:

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

%F n=2: [order 9] for n>10

%F n=3: [order 24] for n>26

%F n=4: [order 49] for n>54

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 26 2013

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Last modified May 22 16:03 EDT 2022. Contains 353957 sequences. (Running on oeis4.)