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A281251
T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
5
0, 0, 0, 0, 0, 0, 1, 12, 12, 1, 2, 139, 443, 139, 2, 9, 1222, 8489, 8489, 1222, 9, 34, 9151, 105368, 197429, 105368, 9151, 34, 124, 63138, 1113148, 3291920, 3291920, 1113148, 63138, 124, 432, 412070, 10598099, 47427679, 76670685, 47427679, 10598099
OFFSET
1,8
COMMENTS
Table starts
....0........0..........0...........1............2.............9............34
....0........0.........12.........139.........1222..........9151.........63138
....0.......12........443........8489.......105368.......1113148......10598099
....1......139.......8489......197429......3291920......47427679.....622370435
....2.....1222.....105368.....3291920.....76670685....1545796513...28420462973
....9.....9151....1113148....47427679...1545796513...43504627489.1115818883427
...34....63138...10598099...622370435..28420462973.1115818883427
..124...412070...94350141..7668286112.491401215701
..432..2585022..800540848.90290912746
.1464.15739317.6552843938
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10
k=2: [order 10] for n>12
k=3: [order 35] for n>45
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..0. .0..0..1..0. .0..1..2..1. .0..1..0..1. .0..1..1..0
..0..1..2..0. .2..0..1..2. .0..2..0..0. .0..2..0..1. .0..2..2..0
..2..2..1..2. .1..2..2..1. .0..1..1..2. .1..2..2..2. .1..0..0..1
..0..1..0..2. .1..0..0..2. .0..2..0..1. .0..1..0..1. .1..2..0..2
CROSSREFS
Column 1 is A280309.
Sequence in context: A038337 A155825 A125509 * A247511 A374989 A097824
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 18 2017
STATUS
approved