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A240783
T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order
12
1, 1, 2, 1, 3, 4, 1, 4, 11, 8, 1, 6, 20, 34, 16, 1, 9, 46, 97, 111, 32, 1, 14, 97, 305, 459, 361, 64, 1, 22, 216, 959, 2167, 2187, 1172, 128, 1, 35, 472, 3033, 10150, 15332, 10442, 3809, 256, 1, 56, 1043, 9581, 47920, 106411, 108509, 49861, 12377, 512, 1, 90, 2296, 30354
OFFSET
1,3
COMMENTS
Table starts
...1.....1.......1........1..........1...........1.............1..............1
...2.....3.......4........6..........9..........14............22.............35
...4....11......20.......46.........97.........216...........472...........1043
...8....34......97......305........959........3033..........9581..........30354
..16...111.....459.....2167......10150.......47920........226532........1071982
..32...361....2187....15332.....106411......746346.......5228820.......36701371
..64..1172...10442...108509....1120383....11677893.....121621207.....1269199948
.128..3809...49861...767834...11791412...182610635....2827515311....43857418181
.256.12377..238068..5434887..124095989..2856212777...65742420202..1515928067679
.512.40218.1136678.38467875.1306056075.44672652785.1528546759636.52397680462958
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) -a(n-3) +4*a(n-4) -4*a(n-5) -3*a(n-6) +a(n-7)
k=4: [order 22]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) -a(n-3)
n=3: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-5)
n=4: [order 15]
n=5: [order 30] for n>34
n=6: [order 94]
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..1..0....0..1..1..0
..1..0..1..0....0..0..1..0....0..1..1..0....1..1..1..0....0..1..1..1
..0..0..1..0....1..0..1..1....1..1..1..0....1..1..1..0....1..0..1..1
..0..1..0..1....1..0..1..1....1..1..0..1....0..1..0..1....1..0..1..1
CROSSREFS
Column 1 is A000079(n-1)
Column 2 is A180762
Row 2 is A001611(n+1)
Sequence in context: A159856 A137649 A180915 * A327083 A104002 A073135
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 12 2014
STATUS
approved