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

1, 1, 1, 2, 5, 2, 5, 27, 27, 5, 14, 193, 461, 193, 14, 41, 1391, 7980, 7980, 1391, 41, 122, 10072, 138562, 332412, 138562, 10072, 122, 365, 72941, 2406061, 13844254, 13844254, 2406061, 72941, 365, 1094, 528283, 41780245, 576606991, 1382959986

Offset

1,4

Comments

Table starts

...1......1.........2.............5...............14..................41

...1......5........27...........193.............1391...............10072

...2.....27.......461..........7980...........138562.............2406061

...5....193......7980........332412.........13844254...........576606991

..14...1391....138562......13844254.......1382959986........138151966465

..41..10072...2406061.....576606991.....138151966465......33101173163229

.122..72941..41780245...24015292771...13800783910238....7931008306049886

.365.528283.725496762.1000221764213.1378639013959376.1900262865283299277

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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

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

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)

k=4: [order 20]

k=5: [order 54]

Example

Some solutions for n=3 k=4
..0..1..2..3....0..1..2..3....0..1..0..2....0..1..0..2....0..1..2..1
..3..2..0..2....1..0..3..0....2..0..2..0....3..2..1..0....3..0..3..2
..2..0..2..1....2..3..0..2....3..2..3..2....1..3..2..1....0..2..0..3

Crossrefs

Column 1 is A007051(n-2)

Column 2 is A240637

Sequence in context: A321577 A268789 A269920 * A240642 A240774 A198604

Adjacent sequences: A240703 A240704 A240705 * A240707 A240708 A240709

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 10 2014

Status

approved