A281693 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 1, 6, 15, 0, 2, 272, 847, 222, 0, 9, 2516, 14575, 19326, 2348, 0, 34, 19168, 172398, 402470, 293814, 21302, 0, 124, 120824, 1900616, 7497214, 8944910, 3714629, 176125, 0, 432, 692320, 17698286, 126719222, 269206287, 173467508, 42265965

Offset

1,8

Comments

Table starts

.0........0..........0............1.............2..............9.............34

.0........0..........6..........272..........2516..........19168.........120824

.0.......15........847........14575........172398........1900616.......17698286

.0......222......19326.......402470.......7497214......126719222.....1847808312

.0.....2348.....293814......8944910.....269206287.....7098401706...164629898128

.0....21302....3714629....173467508....8480641650...352593003706.13101015889336

.0...176125...42265965...3105145787..247006584444.16285953756462

.0..1370378..449985840..52667675560.6815559005187

.0.10206549.4571830360.858903297578

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: [order 12]

k=3: [order 15] for n>20

k=4: [order 48] for n>56

Empirical for row n:

n=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

n=2: [order 12] for n>15

n=3: [order 40] for n>45

Example

Some solutions for n=3 k=4
..0..1..1..0. .0..1..2..2. .0..1..1..0. .0..1..2..0. .0..0..1..2
..2..1..0..0. .2..0..0..0. .1..0..1..0. .1..2..0..1. .2..0..1..2
..2..0..2..2. .1..0..2..0. .1..2..2..1. .0..1..2..1. .1..0..1..1

Crossrefs

Column 2 is A279530.

Row 1 is A280309.

Sequence in context: A263695 A158965 A284075 * A013314 A328339 A019306

Adjacent sequences: A281690 A281691 A281692 * A281694 A281695 A281696

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 27 2017

Status

approved