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A269052
T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.
13
3, 9, 9, 24, 42, 27, 60, 102, 174, 81, 144, 360, 594, 666, 243, 336, 1068, 3078, 3258, 2430, 729, 768, 3288, 13140, 24192, 17346, 8586, 2187, 1728, 9864, 58752, 149358, 183072, 90450, 29646, 6561, 3840, 29472, 253416, 971844, 1643376, 1350672, 464250
OFFSET
1,1
COMMENTS
Table starts
.....3.......9.......24.........60..........144............336.............768
.....9......42......102........360.........1068...........3288............9864
....27.....174......594.......3078........13140..........58752..........253416
....81.....666.....3258......24192.......149358.........971844.........6053094
...243....2430....17346.....183072......1643376.......15547380.......140497512
...729....8586....90450....1350672.....17696520......242861616......3193266318
..2187...29646...464250....9779808....187575858.....3726221592.....71430596250
..6561..100602..2353338...69793968...1964080920....56376679620...1577976495486
.19683..336798.11809746..492374976..20365312416...843461153880..34509932303172
.59049.1115370.58773858.3441051984.209472681102.12504078167988.748499855355192
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
k=5: [order 12] for n>13
k=6: [order 18] for n>19
k=7: [order 38] for n>39
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
n=4: [order 12] for n>14
n=5: [order 20] for n>22
n=6: [order 46] for n>48
n=7: [order 92] for n>94
EXAMPLE
Some solutions for n=4 k=4
..1..2..2..1. .1..2..1..0. .0..1..2..2. .0..1..0..1. .2..1..0..1
..2..2..2..1. .1..2..1..0. .2..1..2..1. .0..1..2..1. .2..1..2..1
..1..2..2..2. .1..0..1..2. .1..2..2..1. .2..1..0..1. .2..1..2..1
..1..2..1..2. .0..2..1..2. .1..2..2..2. .0..1..2..0. .2..1..2..1
CROSSREFS
Column 1 is A000244.
Column 2 is A268622.
Row 1 is A084858.
Sequence in context: A207015 A268809 A268628 * A268971 A267966 A263320
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 18 2016
STATUS
approved