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

Author

R. H. Hardin, Apr 19 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A007581(n-1)

Row 1 is A007051(n-2)

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