A196322 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4

1, 1, 1, 2, 7, 2, 3, 10, 10, 3, 5, 23, 30, 23, 5, 8, 57, 88, 88, 57, 8, 13, 122, 299, 495, 299, 122, 13, 21, 275, 978, 2255, 2255, 978, 275, 21, 34, 623, 3132, 10934, 17093, 10934, 3132, 623, 34, 55, 1394, 10106, 54081, 120633, 120633, 54081, 10106, 1394, 55, 89

Offset

1,4

Comments

Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 4's

Table starts

..1....1......2.......3.........5...........8...........13.............21

..1....7.....10......23........57.........122..........275............623

..2...10.....30......88.......299.........978.........3132..........10106

..3...23.....88.....495......2255.......10934........54081.........264797

..5...57....299....2255.....17093......120633.......879613........6412539

..8..122....978...10934....120633.....1313940.....14115912......152443404

.13..275...3132...54081....879613....14115912....228181579.....3665485997

.21..623..10106..264797...6412539...152443404...3665485997....88027683663

.34.1394..32721.1296124..46525107..1650437009..59089675296..2111492855742

.55.3133.105779.6337697.338253489.17857068383.953116106453.50695941367351

Links

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

Example

Some solutions for n=6 k=4
..0..0..0..2....0..0..0..0....0..0..0..0....2..0..0..0....0..2..0..2
..0..2..2..0....0..0..2..2....2..3..2..0....0..0..0..0....2..2..0..0
..0..2..3..0....0..0..2..0....0..2..2..0....2..3..2..2....0..0..0..0
..0..0..2..0....2..2..3..0....0..0..0..0....0..2..0..0....2..3..2..0
..0..0..2..0....0..0..2..0....2..2..2..0....2..3..0..0....0..2..2..0
..0..0..2..0....0..0..2..0....0..0..2..0....0..2..0..0....2..0..0..2

Crossrefs

Column 1 is A000045

Sequence in context: A196329 A196653 A196343 * A197457 A197307 A196974

Adjacent sequences: A196319 A196320 A196321 * A196323 A196324 A196325

Keyword

nonn,tabl

Author

R. H. Hardin Oct 01 2011

Status

approved