A222541 T(n,k)=Number of nXk 0..1 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order

1, 1, 2, 1, 1, 4, 4, 5, 5, 8, 5, 8, 9, 16, 16, 10, 19, 32, 58, 29, 32, 12, 54, 70, 161, 155, 78, 64, 34, 104, 361, 772, 929, 871, 236, 128, 43, 294, 842, 3293, 3872, 5216, 2393, 638, 256, 101, 665, 4314, 15953, 33612, 44498, 28925, 13852, 1515, 512, 127, 1653, 10268

Offset

1,3

Comments

Table starts

....1.....1.......1.........4...........5..........10...........12...........34

....2.....1.......5.........8..........19..........54..........104..........294

....4.....5.......9........32..........70.........361..........842.........4314

....8....16......58.......161.........772........3293........15953........76735

...16....29.....155.......929........3872.......33612.......155007......1527917

...32....78.....871......5216.......44498......371241......3438351.....32727579

...64...236....2393.....28925......244106.....4214575.....37975912....737541492

..128...638...13852....162141.....2895313....48672973....905224187..17182756329

..256..1515...38685....912903....16220695...567352766..10437983644.408676372689

..512..4345..227848...5173092...193518017..6655462805.254476711315

.1024.11927..638554..29396683..1095187013.78403172647

.2048.32187.3811983.167762776.13140785478

Links

R. H. Hardin, Table of n, a(n) for n = 1..145

Example

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

Crossrefs

Column 1 is A000079(n-1)

Row 1 is A222353

Sequence in context: A129704 A144460 A336996 * A177263 A357050 A197380

Adjacent sequences: A222538 A222539 A222540 * A222542 A222543 A222544

Keyword

nonn,tabl

Author

R. H. Hardin Feb 24 2013

Status

approved