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.

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

R. H. Hardin, Table of n, a(n) for n = 1..84

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: A145877 A283572 A057075 * A327305 A290328 A200682

Adjacent sequences: A281650 A281651 A281652 * A281654 A281655 A281656

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2017

Status

approved