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A281605
T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
11
1, 2, 2, 4, 9, 5, 11, 29, 50, 14, 30, 110, 209, 285, 41, 82, 442, 1283, 1623, 1617, 122, 224, 1708, 8180, 16198, 12413, 9188, 365, 612, 6596, 49572, 167545, 203276, 95623, 52193, 1094, 1672, 25624, 302304, 1626073, 3401430, 2563481, 736757, 296511, 3281, 4568
OFFSET
1,2
COMMENTS
Table starts
....1.......2.........4..........11.............30.............82
....2.......9........29.........110............442...........1708
....5......50.......209........1283...........8180..........49572
...14.....285......1623.......16198.........167545........1626073
...41....1617.....12413......203276........3401430.......52899445
..122....9188.....95623.....2563481.......69506779.....1732267694
..365...52193....736757....32354824.....1421127262....56764280423
.1094..296511...5678559...408458506....29066686772..1860912910152
.3281.1684466..43771933..5156857179...594539026170.61012156448915
.9842.9569425.337417047.65107404580.12161158312943
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: a(n) = 7*a(n-1) +10*a(n-2) -26*a(n-3) -64*a(n-4) -40*a(n-5) for n>6
k=4: [order 16] for n>18
k=5: [order 40] for n>42
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
n=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
n=3: [order 13] for n>15
n=4: [order 55] for n>58
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..0. .0..1..0..2. .0..1..0..1. .0..1..2..2. .0..1..2..0
..1..2..2..1. .0..1..0..2. .1..2..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .2..2..0..1. .1..0..1..2. .0..1..2..1. .2..1..0..1
..2..1..2..1. .0..1..0..2. .1..2..1..0. .1..2..0..1. .0..1..2..1
CROSSREFS
Column 1 is A007051(n-1).
Column 2 is A231413(n-1).
Row 1 is A021006(n-3).
Row 2 is A280853.
Sequence in context: A241130 A019822 A322765 * A199499 A351351 A160126
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 25 2017
STATUS
approved