A231746 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and vertical neighbors

4, 4, 4, 16, 84, 16, 50, 318, 318, 50, 144, 1328, 4430, 1328, 144, 422, 6064, 60806, 60806, 6064, 422, 1268, 26918, 784076, 2154900, 784076, 26918, 1268, 3823, 116909, 9945132, 71742015, 71742015, 9945132, 116909, 3823, 11472, 511264, 126926437

Offset

1,1

Comments

Table starts

....4......4.........16............50..............144..................422

....4.....84........318..........1328.............6064................26918

...16....318.......4430.........60806...........784076..............9945132

...50...1328......60806.......2154900.........71742015...........2426463539

..144...6064.....784076......71742015.......6425495277.........598711367728

..422..26918....9945132....2426463539.....598711367728......155985773478611

.1268.116909..126926437...82701946547...56006640316980....40539474933206048

.3823.511264.1625269595.2814528154294.5220406326242670.10471241201508754882

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

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 19] for n>20

k=3: [order 87] for n>88

Example

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

Crossrefs

Column 1 is A203094 for n>1

Sequence in context: A218181 A231586 A231700 * A275858 A241094 A319257

Adjacent sequences: A231743 A231744 A231745 * A231747 A231748 A231749

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2013

Status

approved