A280902 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 1, 0, 1, 10, 9, 0, 2, 213, 646, 124, 0, 9, 2292, 22568, 22632, 1464, 0, 34, 21762, 492490, 1451655, 610448, 15768, 0, 124, 184076, 9426050, 65348136, 75809243, 14262832, 159920, 0, 432, 1457827, 162640161, 2571528867, 7083739466

Offset

1,8

Comments

Table starts

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

.0........1...........10.............213...............2292...............21762

.0........9..........646...........22568.............492490.............9426050

.0......124........22632.........1451655...........65348136..........2571528867

.0.....1464.......610448........75809243.........7083739466........574982226478

.0....15768.....14262832......3521886844.......684011230518.....114677717497532

.0...159920....304584096....151803173493.....61277484218852...21239418911643829

.0..1554304...6117000704...6210239609889...5208435552362140.3734730743379447607

.0.14632704.117496694272.244458357395448.425813044528570428

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

Formula

Empirical for column k:

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

k=2: [order 6] for n>8

k=3: [order 6] for n>8

k=4: [order 12] for n>14

k=5: [order 24] for n>27

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 15] for n>17

n=3: [order 54] for n>60

Example

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

Crossrefs

Row 1 is A280309.

Sequence in context: A317813 A038310 A318421 * A118768 A318255 A008956

Adjacent sequences: A280899 A280900 A280901 * A280903 A280904 A280905

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2017

Status

approved