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A233082
T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order
13
1, 2, 3, 5, 14, 10, 14, 95, 122, 36, 41, 662, 1985, 1094, 136, 122, 4631, 32414, 41675, 9842, 528, 365, 32414, 529862, 1588262, 875165, 88574, 2080, 1094, 226895, 8662343, 60632429, 77824814, 18378455, 797162, 8256, 3281, 1588262, 141615905
OFFSET
1,2
COMMENTS
Table starts
......1.........2.............5................14....................41
......3........14............95...............662..................4631
.....10.......122..........1985.............32414................529862
.....36......1094.........41675...........1588262..............60632429
....136......9842........875165..........77824814............6938214854
....528.....88574......18378455........3813415862..........793945203881
...2080....797162.....385947545......186857377214........90851753687090
...8256...7174454....8104898435.....9156011483462.....10396235291448605
..32896..64570082..170202867125...448644562689614...1189649113515482414
.131328.581130734.3574260209615.21983583571791062.136132453105625552657
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1) -8*a(n-2)
k=2: a(n) = 10*a(n-1) -9*a(n-2)
k=3: a(n) = 22*a(n-1) -21*a(n-2)
k=4: a(n) = 50*a(n-1) -49*a(n-2)
k=5: a(n) = 118*a(n-1) -411*a(n-2) +294*a(n-3)
k=6: a(n) = 283*a(n-1) -4251*a(n-2) +13573*a(n-3) -9604*a(n-4)
k=7: [order 6]
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2)
n=2: a(n) = 8*a(n-1) -7*a(n-2) for n>3
n=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3) for n>5
n=4: a(n) = 49*a(n-1) -450*a(n-2) +1466*a(n-3) -1853*a(n-4) +789*a(n-5) for n>8
n=5: [order 10] for n>14
n=6: [order 21] for n>26
n=7: [order 52] for n>58
EXAMPLE
Some solutions for n=3 k=4
..0..1..3..1....0..1..3..1....0..0..0..1....0..0..1..1....0..0..1..0
..1..1..3..2....3..2..3..2....2..0..1..0....2..3..1..3....2..3..2..3
..3..3..2..3....3..3..3..2....2..3..1..3....1..1..3..2....1..3..1..0
CROSSREFS
Column 1 is A007582(n-1)
Column 2 is A199560(n-1)
Row 1 is A007051(n-1)
Sequence in context: A370850 A126333 A266192 * A039575 A291923 A283448
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 03 2013
STATUS
approved