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A280673
T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
11
1, 2, 2, 4, 11, 5, 11, 59, 82, 14, 30, 338, 858, 612, 41, 82, 1917, 10205, 12484, 4568, 122, 224, 10893, 119440, 310365, 181640, 34096, 365, 612, 61880, 1401470, 7533245, 9439606, 2642832, 254496, 1094, 1672, 351541, 16438612, 183331502, 474736149
OFFSET
1,2
COMMENTS
Table starts
....1.........2............4..............11...............30................82
....2........11...........59.............338.............1917.............10893
....5........82..........858...........10205...........119440...........1401470
...14.......612........12484..........310365..........7533245.........183331502
...41......4568.......181640.........9439606........474736149.......23952262535
..122.....34096......2642832.......287101721......29920114246.....3130289979912
..365....254496.....38452768......8732086113....1885698283255...409089889172506
.1094...1899584....559481408....265582964074..118845116023725.53463025958093933
.3281..14178688...8140361856...8077601392565.7490149091439288
.9842.105831168.118440917248.245677069239189
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 8*a(n-1) -4*a(n-2) for n>3
k=3: a(n) = 14*a(n-1) +8*a(n-2)
k=4: a(n) = 29*a(n-1) +44*a(n-2) -27*a(n-3) -81*a(n-4) for n>5
k=5: [order 8] for n>9
k=6: [order 20] for n>22
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
n=2: a(n) = 5*a(n-1) +6*a(n-2) -11*a(n-3) -7*a(n-4) +4*a(n-5) for n>6
n=3: [order 18] for n>20
n=4: [order 73] for n>78
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..0. .0..1..0..2. .0..1..0..1. .0..0..1..0. .0..1..1..0
..0..1..2..1. .2..0..2..1. .0..2..1..0. .2..2..1..1. .2..0..2..0
..1..2..0..0. .2..1..0..2. .2..0..2..0. .1..0..2..2. .1..0..1..1
CROSSREFS
Column 1 is A007051(n-1).
Column 2 is A209094.
Row 1 is A021006(n-3).
Sequence in context: A219985 A220800 A220786 * A363385 A280531 A072074
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 07 2017
STATUS
approved