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A230614
T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero
11
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 30, 0, 0, 0, 0, 30, 260, 348, 0, 0, 0, 0, 108, 2358, 7072, 3956, 0, 0, 0, 0, 386, 20430, 149664, 186396, 44916, 0, 0, 0, 0, 1376, 176774, 3023532, 9244260, 4899200, 509978, 0, 0, 0, 0, 4902, 1527918, 61203362
OFFSET
1,12
COMMENTS
Table starts
.0.0.0.......0..........0.............0................0..................0
.0.0.0.......2..........8............30..............108................386
.0.0.0......30........260..........2358............20430.............176774
.0.0.0.....348.......7072........149664..........3023532...........61203362
.0.0.0....3956.....186396.......9244260........434369516........20503681466
.0.0.0...44916....4899200.....570014364......62312057642......6859445695566
.0.0.0..509978..128706852...35145166536....8937075346246...2294186499807542
.0.0.0.5790456.3381000336.2166884610178.1281770005911328.767293632652220616
LINKS
FORMULA
Empirical for column k:
k=4: a(n) = 15*a(n-1) -45*a(n-2) +42*a(n-3) -12*a(n-4) +a(n-5)
k=5: a(n) = 31*a(n-1) -126*a(n-2) +42*a(n-3) +79*a(n-4) -a(n-5) +8*a(n-6) for n>7
k=6: [order 22] for n>23
k=7: [order 39] for n>41
Empirical for row n:
n=2: a(n) = 4*a(n-1) -a(n-2) -2*a(n-3) for n>4
n=3: [order 14] for n>17
n=4: [order 59] for n>63
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..1....0..1..2..0....0..1..2..0....0..1..2..0....0..1..2..0
..2..0..1..2....0..2..1..0....0..2..1..0....2..0..1..2....0..2..1..2
..2..1..0..2....2..0..2..1....1..2..2..1....2..1..0..2....0..1..0..2
..1..2..1..0....1..2..0..2....0..1..0..2....0..0..1..0....2..0..1..0
CROSSREFS
Row 2 is A230269(n-1)
Sequence in context: A350731 A364055 A184366 * A230730 A299905 A225783
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 25 2013
STATUS
approved