A281251 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and 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, 12, 12, 1, 2, 139, 443, 139, 2, 9, 1222, 8489, 8489, 1222, 9, 34, 9151, 105368, 197429, 105368, 9151, 34, 124, 63138, 1113148, 3291920, 3291920, 1113148, 63138, 124, 432, 412070, 10598099, 47427679, 76670685, 47427679, 10598099

Offset

1,8

Comments

Table starts

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

....0........0.........12.........139.........1222..........9151.........63138

....0.......12........443........8489.......105368.......1113148......10598099

....1......139.......8489......197429......3291920......47427679.....622370435

....2.....1222.....105368.....3291920.....76670685....1545796513...28420462973

....9.....9151....1113148....47427679...1545796513...43504627489.1115818883427

...34....63138...10598099...622370435..28420462973.1115818883427

..124...412070...94350141..7668286112.491401215701

..432..2585022..800540848.90290912746

.1464.15739317.6552843938

Links

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

Formula

Empirical for column k:

k=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

k=2: [order 10] for n>12

k=3: [order 35] for n>45

Example

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

Crossrefs

Column 1 is A280309.

Sequence in context: A038337 A155825 A125509 * A247511 A097824 A133208

Adjacent sequences: A281248 A281249 A281250 * A281252 A281253 A281254

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 18 2017

Status

approved