A197529 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 4,4,1,0,1 for x=0,1,2,3,4

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 7, 32, 7, 1, 1, 17, 69, 69, 17, 1, 1, 41, 308, 289, 308, 41, 1, 1, 99, 1444, 2131, 2131, 1444, 99, 1, 1, 239, 5048, 12071, 26282, 12071, 5048, 239, 1, 1, 577, 20265, 74637, 266240, 266240, 74637, 20265, 577, 1, 1, 1393, 83277, 454685

Offset

1,8

Comments

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

Table starts

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

.1....1......3........7.........17...........41.............99..............239

.1....3.....32.......69........308.........1444...........5048............20265

.1....7.....69......289.......2131........12071..........74637...........454685

.1...17....308.....2131......26282.......266240........2818424.........29249599

.1...41...1444....12071.....266240......4538784.......73297686.......1237970513

.1...99...5048....74637....2818424.....73297686.....2095251333......58226014909

.1..239..20265...454685...29249599...1237970513....58226014909....2629509487169

.1..577..83277..2748523..308300414..21169912001..1640490253969..122188777528171

.1.1393.322864.16739531.3239050114.353504327702.46006820800296.5604034945748187

Links

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

Example

Some solutions containing all values 0 to 4 for n=6 k=4
..0..0..0..0....0..3..0..0....0..3..0..0....0..3..0..0....2..1..0..0
..2..1..0..3....3..0..1..2....0..0..1..0....0..0..0..3....1..4..1..0
..1..4..1..0....0..1..4..1....0..1..4..1....0..3..0..0....0..1..0..0
..2..1..0..0....0..2..1..2....0..2..1..2....2..1..2..0....0..0..0..0
..0..0..0..0....3..0..3..0....0..3..0..0....1..4..1..0....0..3..3..0
..0..3..0..0....0..0..0..0....0..0..3..0....2..1..0..0....0..0..0..0

Crossrefs

Column 2 is A001333(n-1)

Sequence in context: A196746 A196904 A197373 * A165795 A287290 A287981

Adjacent sequences: A197526 A197527 A197528 * A197530 A197531 A197532

Keyword

nonn,tabl

Author

R. H. Hardin Oct 16 2011

Status

approved