A266081 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and vertical neighbors differing from itself by exactly one.

1, 1, 1, 2, 1, 2, 1, 4, 4, 1, 1, 1, 4, 1, 1, 2, 1, 6, 6, 1, 2, 1, 4, 5, 5, 5, 4, 1, 1, 1, 12, 7, 7, 12, 1, 1, 2, 1, 10, 26, 29, 26, 10, 1, 2, 1, 4, 16, 23, 29, 29, 23, 16, 4, 1, 1, 1, 21, 35, 55, 78, 55, 35, 21, 1, 1, 2, 1, 31, 64, 115, 146, 146, 115, 64, 31, 1, 2, 1, 4, 42, 99, 221, 364, 466, 364

Offset

1,4

Comments

Table starts

.1.1..2..1...1....2....1.....1......2......1.......1........2........1

.1.1..4..1...1....4....1.....1......4......1.......1........4........1

.2.4..4..6...5...12...10....16.....21.....31......42.......66.......89

.1.1..6..5...7...26...23....35.....64.....99.....161......276......431

.1.1..5..7..29...29...55...115....221....443.....851.....1659.....3318

.2.4.12.26..29...78..146...364....783...1773....4170.....9548....21795

.1.1.10.23..55..146..466..1155...3364...9229...25566....70308...196647

.1.1.16.35.115..364.1155..3907..12510..41683..136701...446548..1484311

.2.4.21.64.221..783.3364.12510..52773.196401..781997..3116201.12334789

.1.1.31.99.443.1773.9229.41683.196401.925875.4351555.20635583.96976290

Links

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

Formula

Empirical for column k:

k=1: a(n) = a(n-3)

k=2: a(n) = a(n-3)

k=3: a(n) = a(n-1) +a(n-3) +a(n-6) -a(n-7) -a(n-9)

k=4: [order 63]

Example

All solutions for n=4 k=4
..0..2..3..2....0..0..0..0....0..0..0..0....2..3..2..0....0..0..0..0
..0..3..4..3....2..3..2..0....0..2..3..2....3..4..3..0....0..0..0..0
..0..2..3..2....3..4..3..0....0..3..4..3....2..3..2..0....0..0..0..0
..0..0..0..0....2..3..2..0....0..2..3..2....0..0..0..0....0..0..0..0

Crossrefs

Sequence in context: A208548 A157333 A002852 * A188440 A216327 A099875

Adjacent sequences: A266078 A266079 A266080 * A266082 A266083 A266084

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2015

Status

approved