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A279925
T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority 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, 1, 1, 0, 0, 0, 3, 15, 15, 3, 6, 142, 474, 142, 6, 24, 1350, 14281, 14281, 1350, 24, 72, 12858, 399487, 1230799, 399487, 12858, 72, 232, 119396, 11023893, 99427182, 99427182, 11023893, 119396, 232, 720, 1095012, 295670293, 7837914954
OFFSET
1,7
COMMENTS
Table starts
....0........1............0..............3................6...............24
....1........0...........15............142.............1350............12858
....0.......15..........474..........14281...........399487.........11023893
....3......142........14281........1230799.........99427182.......7837914954
....6.....1350.......399487.......99427182......23145488444....5222809114196
...24....12858.....11023893.....7837914954....5222809114196.3362092868045434
...72...119396....295670293...601248781220.1145113368668739
..232..1095012...7789959515.45231133438998
..720..9924024.202165948916
.2232.89076240
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>8
k=2: [order 18] for n>19
k=3: [order 54] for n>58
EXAMPLE
Some solutions for n=3 k=4
..0..1..1..1. .0..1..1..1. .0..1..2..0. .0..0..1..2. .0..1..2..0
..1..0..1..0. .2..0..0..2. .2..0..2..2. .1..1..0..0. .2..0..0..2
..0..1..0..1. .1..2..2..2. .0..2..2..1. .1..1..0..2. .2..0..0..1
CROSSREFS
Column 1 is A279300.
Sequence in context: A063628 A280201 A296842 * A279534 A181404 A096672
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 23 2016
STATUS
approved