A197217 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 4,3,2,1,0 for x=0,1,2,3,4

1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 8, 14, 8, 1, 1, 18, 44, 44, 18, 1, 1, 37, 149, 221, 149, 37, 1, 1, 73, 479, 1175, 1175, 479, 73, 1, 1, 151, 1537, 5982, 10210, 5982, 1537, 151, 1, 1, 306, 4971, 30940, 84893, 84893, 30940, 4971, 306, 1, 1, 621, 16088, 160438, 706153

Offset

1,5

Comments

Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2'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...2.....5.......8........18..........37............73.............151

.1...5....14......44.......149.........479..........1537............4971

.1...8....44.....221......1175........5982.........30940..........160438

.1..18...149....1175.....10210.......84893........706153.........5894192

.1..37...479....5982.....84893.....1130812......15034832.......202026037

.1..73..1537...30940....706153....15034832.....322715244......6984694296

.1.151..4971..160438...5894192...202026037....6984694296....242641943340

.1.306.16088..828709..49247065..2712108937..150562726618...8412809597191

.1.621.52020.4285218.411367276.36354079627.3245505223710.291896308327024

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Example

Some solutions for n=6 k=4
..1..3..1..0....0..1..3..1....2..2..2..0....1..3..1..0....0..1..2..2
..0..1..0..0....0..0..1..0....2..0..2..0....0..1..0..0....1..3..2..2
..0..1..3..1....0..0..0..1....2..1..2..2....0..0..0..0....0..1..0..1
..0..0..1..0....0..1..1..3....2..3..1..2....0..1..0..0....0..0..1..3
..2..2..0..0....1..3..0..1....2..1..2..2....1..3..2..2....0..1..0..1
..2..2..0..0....0..1..0..0....2..2..2..0....0..1..2..2....1..3..1..0

Crossrefs

C. A197211 (k=2), A197212 (k=3), A197213 (k=4),..

Sequence in context: A158188 A176625 A197342 * A197242 A375861 A128564

Adjacent sequences: A197214 A197215 A197216 * A197218 A197219 A197220

Keyword

nonn,tabl

Author

R. H. Hardin Oct 11 2011

Status

approved