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A231108 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero 12
0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 8, 0, 0, 0, 20, 48, 42, 0, 0, 0, 68, 286, 438, 208, 0, 0, 0, 230, 1748, 4674, 3936, 1042, 0, 0, 0, 778, 10734, 53530, 75346, 35430, 5208, 0, 0, 0, 2632, 65934, 616562, 1608428, 1217338, 318864, 26042, 0, 0, 0, 8904, 404984, 7084870 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
Table starts
.0.0.....0.......0.........0...........0.............0...............0
.0.0.....2.......6........20..........68...........230.............778
.0.0.....8......48.......286........1748.........10734...........65934
.0.0....42.....438......4674.......53530........616562.........7084870
.0.0...208....3936.....75346.....1608428......34716434.......745738376
.0.0..1042...35430...1217338....48463174....1961000570.....78805506362
.0.0..5208..318864..19662930..1459796386..110728004898...8325135556908
.0.0.26042.2869782.317613674.43973372728.6252665856636.879549454424322
LINKS
FORMULA
Empirical for column k:
k=3: a(n) = 4*a(n-1) +5*a(n-2)
k=4: a(n) = 8*a(n-1) +9*a(n-2)
k=5: a(n) = 14*a(n-1) +35*a(n-2) -4*a(n-3) +4*a(n-4) +32*a(n-5) -32*a(n-6)
k=6: [order 17] for n>18
k=7: [order 32] for n>34
Empirical for row n:
n=2: a(n) = 3*a(n-1) +a(n-2) +a(n-3)
n=3: [order 12] for n>16
n=4: [order 51] for n>56
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..3....0..1..0..1....0..1..2..1....0..1..2..1....0..1..0..3
..2..3..2..3....2..3..2..0....0..3..0..3....0..3..2..1....2..3..1..2
..0..1..0..3....2..0..1..0....0..1..2..1....2..1..0..1....2..0..3..2
..0..3..2..1....3..2..3..2....0..3..2..1....0..3..2..1....3..0..1..0
CROSSREFS
Row 2 is A231057(n-1)
Sequence in context: A028973 A066503 A057385 * A231285 A268729 A182317
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 03 2013
STATUS
approved

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Last modified May 23 18:59 EDT 2024. Contains 372765 sequences. (Running on oeis4.)