A266067 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical, diagonal and antidiagonal neighbors exactly one smaller than itself.

1, 3, 3, 4, 17, 4, 5, 35, 35, 5, 9, 89, 34, 89, 9, 16, 323, 81, 81, 323, 16, 25, 1057, 809, 525, 809, 1057, 25, 39, 3027, 1750, 8262, 8262, 1750, 3027, 39, 64, 9257, 5071, 25663, 154939, 25663, 5071, 9257, 64, 105, 29835, 29256, 148323, 1066148, 1066148, 148323

Offset: 1

Author

R. H. Hardin, Dec 20 2015

Keywords

• nonn
• tabl

Comments

Table starts

...1.....3......4.......5.........9........16........25.........39.........64

...3....17.....35......89.......323......1057......3027.......9257......29835

...4....35.....34......81.......809......1750......5071......29256......93170

...5....89.....81.....525......8262.....25663....148323....1480037....7361668

...9...323....809....8262....154939...1066148..11753249..164649556.1624261580

..16..1057...1750...25663...1066148..11211992.156829155.3678276863

..25..3027...5071..148323..11753249.156829155

..39..9257..29256.1480037.164649556

..64.29835..93170.7361668

.105.92561.300067

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..84

Crossrefs

Column 1 is A195971.

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3) +a(n-4)

k=2: [order 18]

k=3: [order 78]