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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A195971.

Sequence in context: A291873 A118114 A366555 * A378151 A300368 A306521

Adjacent sequences: A266064 A266065 A266066 * A266068 A266069 A266070

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2015

Status

approved