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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
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)