

A230940


T(n,k)=Number of whitesquare subarrays of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero


5



0, 2, 2, 2, 6, 2, 8, 16, 16, 8, 8, 48, 34, 48, 8, 42, 146, 232, 232, 146, 42, 42, 438, 522, 1242, 522, 438, 42, 208, 1312, 3768, 6896, 6896, 3768, 1312, 208, 208, 3936, 8450, 37984, 28216, 37984, 8450, 3936, 208, 1042, 11810, 60824, 208172, 396950, 396950
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OFFSET

1,2


COMMENTS

Table starts
...0....2.....2.......8........8........42.........42..........208
...2....6....16......48......146.......438.......1312.........3936
...2...16....34.....232......522......3768.......8450........60824
...8...48...232....1242.....6896.....37984.....208172......1142054
...8..146...522....6896....28216....396950....1604098.....22368688
..42..438..3768...37984...396950...4092246...41991510....431437274
..42.1312..8450..208172..1604098..41991510..318984080...8279222070
.208.3936.60824.1142054.22368688.431437274.8279222070.159130979900


LINKS



FORMULA

Empirical for column k:
k=1: a(n) = 4*a(n2) +5*a(n4)
k=2: a(n) = 3*a(n1) a(n2) +3*a(n3)
k=3: a(n) = 16*a(n2) +3*a(n4) 10*a(n6) +24*a(n8) 16*a(n10)
k=4: [order 17]
k=5: [order 44]
k=6: [order 71]


EXAMPLE

Some solutions for n=4 k=4
..0..x..0..x..0..x....0..x..0..x..3..x....0..x..0..x..2..x....0..x..0..x..0..x
..x..1..x..3..x..1....x..1..x..2..x..0....x..1..x..3..x..1....x..1..x..1..x..3
..2..x..0..x..2..x....2..x..0..x..1..x....2..x..2..x..0..x....2..x..2..x..0..x
..x..3..x..3..x..3....x..3..x..3..x..3....x..3..x..1..x..3....x..3..x..3..x..3
..2..x..2..x..0..x....2..x..2..x..0..x....2..x..0..x..2..x....0..x..2..x..0..x
..x..1..x..1..x..3....x..1..x..1..x..3....x..3..x..1..x..1....x..1..x..1..x..3


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STATUS

approved



