A241328 T(n,k)=Number of nXk 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order

1, 1, 2, 2, 8, 5, 5, 59, 85, 15, 14, 530, 2344, 1030, 51, 41, 4877, 68935, 95144, 13011, 187, 122, 45057, 2034543, 8949808, 3875244, 165924, 715, 365, 416533, 60066019, 842185933, 1162535788, 157912026, 2121033, 2795, 1094, 3851085, 1773370241

Offset

1,3

Comments

Table starts

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

...2.......8.........59............530..............4877.................45057

...5......85.......2344..........68935...........2034543..............60066019

..15....1030......95144........8949808.........842185933...........79254376889

..51...13011....3875244.....1162535788......348722168314.......104609549355169

.187..165924..157912026...151022716125...144410575985227....138095118530911728

.715.2121033.6435036610.19619065042282.59802363257355728.182299462522915741748

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

k=2: [order 9] for n>10

k=3: [order 15]

k=4: [order 53]

Empirical for row n:

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

n=2: a(n) = 12*a(n-1) -26*a(n-2) +2*a(n-3) +28*a(n-4) -6*a(n-5) -9*a(n-6) for n>8

n=3: [order 11] for n>13

n=4: [order 36] for n>38

Example

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

Crossrefs

Column 1 is A007581(n-1)

Row 1 is A007051(n-2)

Sequence in context: A075103 A021818 A336198 * A223041 A024558 A238452

Adjacent sequences: A241325 A241326 A241327 * A241329 A241330 A241331

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 19 2014

Status

approved