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

Author

R. H. Hardin, Apr 14 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A206687

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]