A279805 T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 2, 2, 4, 22, 22, 4, 14, 196, 740, 196, 14, 40, 1848, 19376, 19376, 1848, 40, 120, 16720, 507986, 1476500, 507986, 16720, 120, 352, 149392, 12910722, 110514378, 110514378, 12910722, 149392, 352, 1032, 1317720, 323712032, 8028037200

Offset

1,4

Comments

Table starts

....0........0............2..............4..............14...............40

....0........2...........22............196............1848............16720

....2.......22..........740..........19376..........507986.........12910722

....4......196........19376........1476500.......110514378.......8028037200

...14.....1848.......507986......110514378.....23500346624....4849917013896

...40....16720.....12910722.....8028037200...4849917013896.2840019147221278

..120...149392....323712032...573336320344.982389352238899

..352..1317720...8013623436.40364489132724

.1032.11508016.196400852184

.3008.99674848

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

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

k=2: [order 12]

k=3: [order 36] for n>37

Example

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

Crossrefs

Column 1 is A279322.

Sequence in context: A107902 A142974 A259856 * A123914 A347356 A285441

Adjacent sequences: A279802 A279803 A279804 * A279806 A279807 A279808

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2016

Status

approved