A196436 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 2,1,0,3,4 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, 7358, 5311, 1801, 369, 28, 41, 769, 5219, 21803, 42604, 42604, 21803, 5219, 769, 41, 60, 1600, 15133, 89640

Offset

1,2

Comments

Every 0 is next to zero 2's, every 1 is next to one 1's, every 2 is next to two 2's, every 3 is next to three 3's, every 4 is next to four 4'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.....7358......42604......246463.......1427278

..9...85...621....5311....42604.....349511.....2856711......23313460

.13..178..1801...21803...246463....2856711....32855368.....378154308

.19..369..5219...89640..1427278...23313460...378154308....6141909014

.28..769.15133..369032..8257394..190423461..4356726770...99754551113

.41.1600.43867.1517961.47782109.1555501171.50163397373.1619739781963

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Example

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

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A105309(n+1).

Diagonal is A145773.

Sequence in context: A014430 A360196 A225622 * A197199 A295120 A196957

Adjacent sequences: A196433 A196434 A196435 * A196437 A196438 A196439

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 02 2011

Status

approved