A197079 T(n,k) = Number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,2,4,0 for x=0,1,2,3,4.

1, 2, 2, 3, 6, 3, 4, 13, 13, 4, 6, 34, 51, 34, 6, 9, 81, 205, 205, 81, 9, 13, 199, 812, 1407, 812, 199, 13, 19, 487, 3295, 9492, 9492, 3295, 487, 19, 28, 1190, 13286, 65251, 109286, 65251, 13286, 1190, 28, 41, 2910, 53418, 445506, 1282123, 1282123, 445506, 53418

Offset

1,2

Comments

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

Table starts:

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

..2....6.....13........34..........81...........199.............487

..3...13.....51.......205.........812..........3295...........13286

..4...34....205......1407........9492.........65251..........445506

..6...81....812......9492......109286.......1282123........14895018

..9..199...3295.....65251.....1282123......25822213.......513380599

.13..487..13286....445506....14895018.....513380599.....17446576240

.19.1190..53418...3041309...173097490...10204673140....592290047724

.28.2910.215148..20782756..2014367937..203083535620..20128502440024

.41.7115.866828.142011656.23437273689.4041562578683.683993118482402

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Example

Some solutions for n=6 k=4:
..0..0..1..1....2..2..0..0....1..1..0..1....0..0..1..1....0..0..1..0
..0..0..0..0....2..2..1..1....0..0..0..1....0..0..0..0....0..0..1..0
..0..0..0..1....1..1..0..0....0..0..0..0....2..2..2..2....0..0..2..2
..0..4..0..1....0..0..0..0....0..4..0..0....2..1..1..2....1..0..2..2
..0..0..4..0....0..4..0..1....1..0..0..1....2..0..0..2....1..0..1..1
..0..0..0..0....0..0..0..1....1..0..0..1....2..2..2..2....0..0..0..0

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A196906.

Sequence in context: A210220 A075196 A196912 * A208340 A308503 A196967

Adjacent sequences: A197076 A197077 A197078 * A197080 A197081 A197082

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 09 2011

Status

approved