A266055 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than or equal to itself.

1, 3, 1, 2, 7, 1, 7, 12, 35, 1, 19, 58, 20, 176, 1, 35, 598, 302, 54, 819, 1, 77, 4427, 10310, 4203, 120, 3927, 1, 176, 26350, 127492, 624720, 41919, 284, 18711, 1, 377, 164148, 1590691, 14337385, 27764427, 406412, 660, 89179, 1, 819, 1074794, 20375630

Offset

1,2

Comments

Table starts

.1....3...2......7.........19...........35.............77...............176

.1....7..12.....58........598.........4427..........26350............164148

.1...35..20....302......10310.......127492........1590691..........20375630

.1..176..54...4203.....624720.....14337385......454759923.......21604580859

.1..819.120..41919...27764427...1550545435...117167373425....15587739999833

.1.3927.284.406412.1354845965.162959704686.30258541759225.12768467508350730

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +7*a(n-2) +7*a(n-3) -a(n-4)

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

k=4: [order 10] for n>12

k=5: [order 37] for n>40

k=6: [order 85] for n>89

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]

n=3: [order 94] for n>99

Example

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

Crossrefs

Row 1 is A196537.

Sequence in context: A331789 A308001 A191862 * A074305 A151855 A186366

Adjacent sequences: A266052 A266053 A266054 * A266056 A266057 A266058

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2015

Status

approved