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R. H. Hardin, <a href="/A266081/b266081.txt">Table of n, a(n) for n = 1..264</a>

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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

1,4

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

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]

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

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nonn,tabl

R. H. Hardin, Dec 20 2015

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