A197199 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 4,1,3,2,0 for x=0,1,2,3,4

1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 6, 20, 25, 20, 6, 9, 41, 75, 75, 41, 9, 13, 85, 213, 314, 213, 85, 13, 19, 178, 621, 1283, 1283, 621, 178, 19, 28, 369, 1801, 5311, 7363, 5311, 1801, 369, 28, 41, 769, 5219, 21803, 42664, 42664, 21803, 5219, 769, 41, 60, 1600, 15133, 89640

Offset

1,2

Comments

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

Table starts

..1....2.....3.......4........6..........9..........13............19

..2....5.....9......20.......41.........85.........178...........369

..3....9....25......75......213........621........1801..........5219

..4...20....75.....314.....1283.......5311.......21803.........89640

..6...41...213....1283.....7363......42664......247053.......1431868

..9...85...621....5311....42664.....350711.....2873141......23497244

.13..178..1801...21803...247053....2873141....33176391.....383262156

.19..369..5219...89640..1431868...23497244...383262156....6258308430

.28..769.15133..369032..8291425..192348965..4432780869..102222467201

.41.1600.43867.1517961.48020216.1574634137.51234398070.1669087121069

Links

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

Example

Some solutions for n=6 k=4
..0..1..1..0....1..1..0..1....0..0..0..0....0..1..0..0....1..0..0..1
..1..0..0..1....0..0..0..1....0..1..1..0....0..1..0..0....1..0..0..1
..1..0..0..1....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....1..0..0..0....1..0..0..1....1..1..0..0....1..1..0..0
..0..0..0..0....1..0..0..0....0..1..0..1....0..0..0..1....0..0..0..0
..0..0..0..0....0..0..1..1....0..1..0..0....0..0..0..1....0..0..1..1

Crossrefs

Column 1 is A000930(n+1)

Column 2 is A105309(n+1)

Column 3 is A196431

Column 4 is A196432

Sequence in context: A360196 A225622 A196436 * A295120 A196957 A124727

Adjacent sequences: A197196 A197197 A197198 * A197200 A197201 A197202

Keyword

nonn,tabl

Author

R. H. Hardin Oct 11 2011

Status

approved