login
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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 03 2013
STATUS
approved