A231586 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors

4, 4, 4, 16, 28, 16, 50, 124, 124, 50, 144, 602, 2352, 602, 144, 422, 2776, 32650, 32650, 2776, 422, 1268, 12922, 381076, 1245468, 381076, 12922, 1268, 3823, 60720, 5618444, 38768838, 38768838, 5618444, 60720, 3823, 11472, 286047, 82479418, 1453028265

Offset

1,1

Comments

Table starts

.....4.......4...........16...............50................144

.....4......28..........124..............602...............2776

....16.....124.........2352............32650.............381076

....50.....602........32650..........1245468...........38768838

...144....2776.......381076.........38768838.........2912579313

...422...12922......5618444.......1453028265.......260228939106

..1268...60720.....82479418......57099276134.....24813120747919

..3823..286047...1142396851....2144257250786...2275463989704521

.11472.1335296..16061107556...79701582158514.205616812796559119

.34350.6256326.231334122108.3015862229160377

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8

k=2: [order 16]

k=3: [order 72] for n>73

Example

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

Crossrefs

Column 1 is A203094 for n>1

Sequence in context: A218651 A298730 A218181 * A231700 A231746 A275858

Adjacent sequences: A231583 A231584 A231585 * A231587 A231588 A231589

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 11 2013

Status

approved