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A281653
T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
10
0, 0, 0, 1, 4, 0, 2, 70, 46, 0, 8, 400, 985, 384, 0, 28, 2128, 7986, 10572, 2894, 0, 94, 10512, 67884, 135444, 104815, 20444, 0, 304, 49352, 519656, 1887730, 2159590, 982206, 138944, 0, 960, 225024, 3804074, 23075928, 48871479, 32771472, 8921869
OFFSET
1,5
COMMENTS
Table starts
.0........0..........1...........2............8............28............94
.0........4.........70.........400.........2128.........10512.........49352
.0.......46........985........7986........67884........519656.......3804074
.0......384......10572......135444......1887730......23075928.....270969324
.0.....2894.....104815.....2159590.....48871479.....955490042...18092139475
.0....20444.....982206....32771472...1205962480...37763465272.1154703692514
.0...138944....8921869...483655876..28906723792.1449940771656
.0...918744...79152992..6987992320.677956602812
.0..5954690..690169163.99358947608
.0.38005496.5936924514
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: [order 8]
k=3: [order 10] for n>13
k=4: [order 32] for n>37
Empirical for row n:
n=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7
n=2: [order 8] for n>9
n=3: [order 26] for n>29
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..2. .0..1..0..0. .0..1..0..2. .0..0..1..2. .0..1..0..1
..2..1..1..1. .0..2..2..1. .0..2..0..2. .1..1..1..2. .2..0..2..1
..0..0..2..1. .0..2..0..0. .1..0..1..2. .2..0..2..0. .0..1..0..2
..2..1..2..1. .0..2..1..1. .2..0..1..2. .1..1..2..0. .1..2..0..2
CROSSREFS
Column 2 is A279523.
Row 1 is A280279.
Sequence in context: A373984 A283572 A057075 * A327305 A290328 A200682
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 26 2017
STATUS
approved