A231049 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 14, 2, 0, 0, 32, 50, 10, 0, 0, 100, 128, 410, 22, 0, 0, 428, 644, 2080, 2430, 70, 0, 0, 1616, 5100, 20050, 18688, 16198, 186, 0, 0, 5784, 33696, 310804, 344136, 209440, 103042, 538, 0, 0, 21248, 211032, 4110640, 10631552, 7293728

Offset

1,5

Comments

Table starts

.0....0........0..........0.............0................0..................0

.0....2.......14.........32...........100..............428...............1616

.0....2.......50........128...........644.............5100..............33696

.0...10......410.......2080.........20050...........310804............4110640

.0...22.....2430......18688........344136.........10631552..........274004640

.0...70....16198.....209440.......7293728........448752816........22665736960

.0..186...103042....2150784.....142466422......17477913984......1729680196768

.0..538...667690...22847008....2871061676.....702369644524....136193662172048

.0.1494..4294910..239510016...57167235796...27889180833188..10596817937397952

.0.4230.27706854.2523778080.1143545760606.1112507026382520.828295717027921136

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

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

k=3: a(n) = 3*a(n-1) +19*a(n-2) +19*a(n-3) +12*a(n-4) -8*a(n-5) +8*a(n-6)

k=4: a(n) = 8*a(n-1) +33*a(n-2) -68*a(n-3)

k=5: [order 36]

k=6: [order 93]

Empirical for row n:

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

n=3: [order 10] for n>11

n=4: [order 31] for n>32

Example

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

Crossrefs

Column 2 is A230893

Sequence in context: A231031 A061848 A193294 * A231080 A231246 A216991

Adjacent sequences: A231046 A231047 A231048 * A231050 A231051 A231052

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved