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A230935
T(n,k)=Number of black-square 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
9
2, 2, 2, 8, 6, 8, 8, 16, 16, 8, 42, 48, 102, 48, 42, 42, 146, 232, 232, 146, 42, 208, 438, 1682, 1242, 1682, 438, 208, 208, 1312, 3768, 6896, 6896, 3768, 1312, 208, 1042, 3936, 27106, 37984, 98296, 37984, 27106, 3936, 1042, 1042, 11810, 60824, 208172, 396950
OFFSET
1,1
COMMENTS
Table starts
...2....2.....8.......8.......42........42........208..........208
...2....6....16......48......146.......438.......1312.........3936
...8...16...102.....232.....1682......3768......27106........60824
...8...48...232....1242.....6896.....37984.....208172......1142054
..42..146..1682....6896....98296....396950....5528862.....22368688
..42..438..3768...37984...396950...4092246...41991510....431437274
.208.1312.27106..208172..5528862..41991510.1088383766...8279222070
.208.3936.60824.1142054.22368688.431437274.8279222070.159130979900
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-2) +5*a(n-4)
k=2: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3)
k=3: a(n) = 16*a(n-2) +3*a(n-4) -10*a(n-6) +24*a(n-8) -16*a(n-10)
k=4: [order 17]
k=5: [order 44]
k=6: [order 71]
EXAMPLE
Some solutions for n=4 k=4
..x..0..x..0..x..2....x..0..x..2..x..2....x..0..x..2..x..2....x..0..x..0..x..2
..3..x..1..x..3..x....1..x..1..x..3..x....1..x..3..x..3..x....3..x..1..x..3..x
..x..0..x..2..x..2....x..2..x..2..x..0....x..2..x..0..x..2....x..2..x..2..x..0
..3..x..1..x..3..x....3..x..1..x..1..x....1..x..3..x..1..x....1..x..3..x..1..x
..x..0..x..2..x..0....x..0..x..2..x..0....x..2..x..0..x..2....x..2..x..0..x..0
..3..x..3..x..1..x....3..x..1..x..3..x....1..x..1..x..3..x....1..x..3..x..3..x
CROSSREFS
Sequence in context: A085484 A326480 A116585 * A008293 A185811 A011140
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 01 2013
STATUS
approved