A281605 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 9, 5, 11, 29, 50, 14, 30, 110, 209, 285, 41, 82, 442, 1283, 1623, 1617, 122, 224, 1708, 8180, 16198, 12413, 9188, 365, 612, 6596, 49572, 167545, 203276, 95623, 52193, 1094, 1672, 25624, 302304, 1626073, 3401430, 2563481, 736757, 296511, 3281, 4568

Offset

1,2

Comments

Table starts

....1.......2.........4..........11.............30.............82

....2.......9........29.........110............442...........1708

....5......50.......209........1283...........8180..........49572

...14.....285......1623.......16198.........167545........1626073

...41....1617.....12413......203276........3401430.......52899445

..122....9188.....95623.....2563481.......69506779.....1732267694

..365...52193....736757....32354824.....1421127262....56764280423

.1094..296511...5678559...408458506....29066686772..1860912910152

.3281.1684466..43771933..5156857179...594539026170.61012156448915

.9842.9569425.337417047.65107404580.12161158312943

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2)

k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5

k=3: a(n) = 7*a(n-1) +10*a(n-2) -26*a(n-3) -64*a(n-4) -40*a(n-5) for n>6

k=4: [order 16] for n>18

k=5: [order 40] for n>42

Empirical for row n:

n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4

n=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5

n=3: [order 13] for n>15

n=4: [order 55] for n>58

Example

Some solutions for n=4 k=4
..0..0..1..0. .0..1..0..2. .0..1..0..1. .0..1..2..2. .0..1..2..0
..1..2..2..1. .0..1..0..2. .1..2..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .2..2..0..1. .1..0..1..2. .0..1..2..1. .2..1..0..1
..2..1..2..1. .0..1..0..2. .1..2..1..0. .1..2..0..1. .0..1..2..1

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A231413(n-1).

Row 1 is A021006(n-3).

Row 2 is A280853.

Sequence in context: A241130 A019822 A322765 * A199499 A351351 A160126

Adjacent sequences: A281602 A281603 A281604 * A281606 A281607 A281608

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2017

Status

approved