A265981 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors less than itself.

1, 3, 1, 5, 23, 1, 11, 117, 123, 1, 26, 583, 1267, 809, 1, 55, 5554, 11573, 13894, 5274, 1, 119, 52555, 320641, 282056, 262258, 33923, 1, 263, 405165, 8061815, 40743954, 8935989, 3699605, 219807, 1, 573, 3187023, 133236904, 3698768651, 5155545324

Offset

1,2

Comments

Table starts

.1........3...........5...........11.............26..............55

.1.......23.........117..........583...........5554...........52555

.1......123........1267........11573.........320641.........8061815

.1......809.......13894.......282056.......40743954......3698768651

.1.....5274......262258......8935989.....5155545324...1978988798923

.1....33923.....3699605....250833288...620145580463.809078767234538

.1...219807....50337359...7041080382.79392682076391

.1..1424725...795864688.208041110790

.1..9226721.11746148349

.1.59782080

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

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

k=2: [order 15]

k=3: [order 35] for n>36

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)

n=2: [order 26]

Example

Some solutions for n=3 k=4
..0..4..2..0....0..0..0..1....2..1..4..1....0..0..1..2....2..0..4..1
..1..0..0..3....3..0..6..0....3..0..0..1....0..6..1..3....3..0..0..0
..1..4..2..1....1..2..0..0....2..1..4..1....0..4..0..1....0..0..4..1

Crossrefs

Column 2 is A196424.

Row 1 is A196423.

Sequence in context: A187369 A039512 A140825 * A037280 A352009 A324204

Adjacent sequences: A265978 A265979 A265980 * A265982 A265983 A265984

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2015

Status

approved