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A240706 T(n,k)=Number of nXk 0..3 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order 7

%I

%S 1,1,1,2,5,2,5,27,27,5,14,193,461,193,14,41,1391,7980,7980,1391,41,

%T 122,10072,138562,332412,138562,10072,122,365,72941,2406061,13844254,

%U 13844254,2406061,72941,365,1094,528283,41780245,576606991,1382959986

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order

%C Table starts

%C ...1......1.........2.............5...............14..................41

%C ...1......5........27...........193.............1391...............10072

%C ...2.....27.......461..........7980...........138562.............2406061

%C ...5....193......7980........332412.........13844254...........576606991

%C ..14...1391....138562......13844254.......1382959986........138151966465

%C ..41..10072...2406061.....576606991.....138151966465......33101173163229

%C .122..72941..41780245...24015292771...13800783910238....7931008306049886

%C .365.528283.725496762.1000221764213.1378639013959376.1900262865283299277

%H R. H. Hardin, <a href="/A240706/b240706.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

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

%F k=2: a(n) = 6*a(n-1) +10*a(n-2) -6*a(n-3) -9*a(n-4) for n>6

%F k=3: a(n) = 15*a(n-1) +40*a(n-2) +22*a(n-3) -60*a(n-4) -40*a(n-5) -21*a(n-6) +45*a(n-7)

%F k=4: [order 20]

%F k=5: [order 54]

%e Some solutions for n=3 k=4

%e ..0..1..2..3....0..1..2..3....0..1..0..2....0..1..0..2....0..1..2..1

%e ..3..2..0..2....1..0..3..0....2..0..2..0....3..2..1..0....3..0..3..2

%e ..2..0..2..1....2..3..0..2....3..2..3..2....1..3..2..1....0..2..0..3

%Y Column 1 is A007051(n-2)

%Y Column 2 is A240637

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Apr 10 2014

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)