A231382 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

2, 2, 2, 4, 10, 4, 7, 21, 21, 7, 12, 48, 93, 48, 12, 21, 113, 378, 378, 113, 21, 37, 261, 1519, 2539, 1519, 261, 37, 65, 601, 6126, 17363, 17363, 6126, 601, 65, 114, 1390, 24747, 120124, 209118, 120124, 24747, 1390, 114, 200, 3216, 99964, 830890, 2547810

Offset: 1

Author

R. H. Hardin, Nov 08 2013

Keywords

• nonn
• tabl

Comments

Table starts

...2....2.......4.........7..........12.............21...............37

...2...10......21........48.........113............261..............601

...4...21......93.......378........1519...........6126............24747

...7...48.....378......2539.......17363.........120124...........830890

..12..113....1519.....17363......209118........2547810.........30936914

..21..261....6126....120124.....2547810.......54485279.......1157805351

..37..601...24747....830890....30936914.....1157805351......42978519280

..65.1390...99964...5746499...375620622....24615811883....1597438228604

.114.3216..403743..39745115..4560995236...523548909308...59402875813957

.200.7435.1630662.274872588.55375119088.11133382117666.2208383979206654

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 1 is A005251(n+2)

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4

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

k=3: [order 10] for n>11

k=4: [order 19] for n>20

k=5: [order 46] for n>47