A196989 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 2,3,4,1,0 for x=0,1,2,3,4

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 5, 10, 5, 1, 1, 9, 25, 25, 9, 1, 1, 17, 81, 113, 81, 17, 1, 1, 31, 242, 547, 547, 242, 31, 1, 1, 57, 707, 2499, 4244, 2499, 707, 57, 1, 1, 105, 2095, 11647, 31791, 31791, 11647, 2095, 105, 1, 1, 193, 6224, 54845, 242602, 389518, 242602

Offset

1,8

Comments

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

Table starts

.1...1.....1.......1.........1..........1............1..............1

.1...1.....3.......5.........9.........17...........31.............57

.1...3....10......25........81........242..........707...........2095

.1...5....25.....113.......547.......2499........11647..........54845

.1...9....81.....547......4244......31791.......242602........1838579

.1..17...242....2499.....31791.....389518......4743311.......58038517

.1..31...707...11647....242602....4743311.....93411402.....1863379223

.1..57..2095...54845...1838579...58038517...1863379223....60168452277

.1.105..6224..256395..13941719..713190410..37097158961..1938441718877

.1.193.18499.1198317.105949190.8761030047.737372275936.62562309931101

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Example

Some solutions for n=6 k=4
..0..1..3..1....1..3..1..0....0..0..0..1....0..0..1..0....0..1..0..0
..0..0..1..0....1..1..0..0....0..0..1..3....0..1..3..0....0..3..1..1
..0..0..0..0....3..1..0..1....0..0..0..1....0..0..1..0....0..1..1..3
..0..1..3..1....1..0..1..3....0..0..4..0....1..0..0..0....0..1..0..1
..0..0..1..0....1..3..1..1....0..4..0..0....3..1..0..0....0..3..1..0
..0..0..0..0....0..1..0..0....0..0..0..0....1..0..0..0....0..1..0..0

Crossrefs

Column 2 is A000213

Sequence in context: A132729 A196493 A251634 * A034871 A333758 A015109

Adjacent sequences: A196986 A196987 A196988 * A196990 A196991 A196992

Keyword

nonn,tabl

Author

R. H. Hardin Oct 08 2011

Status

approved