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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.
14
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 20 2015
STATUS
approved