A231515 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors

2, 2, 2, 4, 6, 4, 7, 14, 14, 7, 12, 35, 78, 35, 12, 21, 90, 343, 343, 90, 21, 37, 225, 1537, 2594, 1537, 225, 37, 65, 569, 7505, 19435, 19435, 7505, 569, 65, 114, 1441, 35872, 158061, 256846, 158061, 35872, 1441, 114, 200, 3640, 168887, 1275558, 3691558

Offset

1,1

Comments

Table starts

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

...2....6......14........35...........90............225..............569

...4...14......78.......343.........1537...........7505............35872

...7...35.....343......2594........19435.........158061..........1275558

..12...90....1537.....19435.......256846........3691558.........51741521

..21..225....7505....158061......3691558.......97188562.......2438335793

..37..569...35872...1275558.....51741521.....2438335793.....108221463798

..65.1441..168887..10130742....714951561....59978232085....4680280632866

.114.3640..800573..80645991...9949033842..1495872774439..205954365382497

.200.9208.3806573.644138583.138737920339.37400468849958.9095707696345723

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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) = 2*a(n-1) +a(n-2) +3*a(n-3) -4*a(n-4) -2*a(n-5) -4*a(n-6)

k=3: [order 16] for n>17

k=4: [order 34] for n>35

Example

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

Crossrefs

Column 1 is A005251(n+2)

Sequence in context: A342271 A240433 A217637 * A231544 A086420 A328106

Adjacent sequences: A231512 A231513 A231514 * A231516 A231517 A231518

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 09 2013

Status

approved