A231651 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors

3, 3, 3, 9, 35, 9, 22, 104, 104, 22, 51, 341, 920, 341, 51, 121, 1189, 7682, 7682, 1189, 121, 292, 4040, 61574, 137961, 61574, 4040, 292, 704, 13560, 490760, 2412274, 2412274, 490760, 13560, 704, 1691, 45803, 3929027, 42882766, 96014413, 42882766

Offset

1,1

Comments

Table starts

....3......3..........9............22................51..................121

....3.....35........104...........341..............1189.................4040

....9....104........920..........7682.............61574...............490760

...22....341.......7682........137961...........2412274.............42882766

...51...1189......61574.......2412274..........96014413...........3936913977

..121...4040.....490760......42882766........3936913977.........374409597564

..292..13560....3929027.....765163605......161357952814.......35384751611050

..704..45803...31501117...13643499478.....6602715583511.....3335789961947404

.1691.155131..252454167..243317286312...270337779895196...314852421269523851

.4059.524683.2022844426.4340128403053.11069019817530645.29721381118553717447

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

k=2: [order 11] for n>12

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

Example

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

Crossrefs

Column 1 is A202882 for n>1

Sequence in context: A180439 A298315 A299189 * A160589 A097707 A240533

Adjacent sequences: A231648 A231649 A231650 * A231652 A231653 A231654

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2013

Status

approved