A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order

1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 57, 36, 8, 16, 116, 289, 289, 116, 16, 32, 376, 1485, 2362, 1485, 376, 32, 64, 1216, 7609, 19065, 19065, 7609, 1216, 64, 128, 3936, 38981, 154858, 245268, 154858, 38981, 3936, 128, 256, 12736, 199761, 1255585, 3146755

Offset

1,4

Comments

Table starts

...1.....1.......2.........4...........8.............16...............32

...1.....4......11........36.........116............376.............1216

...2....11......57.......289........1485...........7609............38981

...4....36.....289......2362.......19065.........154858..........1255585

...8...116....1485.....19065......245268........3146755.........40424861

..16...376....7609....154858.....3146755.......64074526.......1302610899

..32..1216...38981...1255585....40424861.....1302610899......41971040844

..64..3936..199761..10186158...519218802....26501432610....1352138182759

.128.12736.1023597..82615013..6669141957...539075345618...43565815810587

.256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)

k=4: [order 16]

k=5: [order 48]

Example

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

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A206687

Sequence in context: A298242 A282283 A288416 * A241108 A151706 A055372

Adjacent sequences: A240890 A240891 A240892 * A240894 A240895 A240896

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 14 2014

Status

approved