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A262420
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.
14
2, 0, 5, 6, 4, 10, 0, 45, 12, 21, 22, 114, 270, 48, 42, 0, 709, 1260, 1701, 144, 85, 86, 2892, 15310, 18228, 10206, 468, 170, 0, 15293, 124572, 428301, 200880, 61965, 1404, 341, 342, 72370, 1299070, 7577424, 9401742, 2353338, 371790, 4320, 682, 0, 367125
OFFSET
1,1
COMMENTS
Table starts
....2.....0........6...........0.............22.................0
....5.....4.......45.........114............709..............2892
...10....12......270........1260..........15310............124572
...21....48.....1701.......18228.........428301...........7577424
...42...144....10206......200880........9401742.........326005344
...85...468....61965.....2353338......220808869.......15231780324
..170..1404...371790....25901100.....4856629870......655089996204
..341..4320..2237301...289462380...108673357501....28755516792360
..682.12960.13423806..3184570800..2390753728462..1236553617638640
.1365.39204.80601885.35172555474.52824430238229.53446495303862172
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -9*a(n-3)
k=3: a(n) = 6*a(n-1) +9*a(n-2) -54*a(n-3)
k=4: [order 7]
k=5: [order 11]
k=6: [order 13]
k=7: [order 19]
Empirical for row n:
n=1: a(n) = 5*a(n-2) -4*a(n-4)
n=2: a(n) = 5*a(n-1) +12*a(n-2) -60*a(n-3) -39*a(n-4) +195*a(n-5) +28*a(n-6) -140*a(n-7)
n=3: [order 9]
n=4: [order 11]
n=5: [order 11]
n=6: [order 17]
n=7: [order 21]
EXAMPLE
Some solutions for n=4 k=4
..1..1..0..1..1....1..1..1..1..0....0..0..1..1..0....1..1..0..0..0
..1..1..0..1..1....0..0..1..1..0....1..0..0..1..0....1..0..0..1..0
..1..0..1..0..1....1..1..1..1..0....1..1..1..1..0....0..0..1..1..0
..1..1..1..1..0....1..1..0..0..0....1..0..1..0..1....1..1..0..1..1
..1..0..1..0..1....1..0..1..0..1....0..0..0..0..0....0..1..1..0..0
CROSSREFS
Column 1 is A000975(n+1).
Row 1 is A047849((n+1)/2) for odd n.
Sequence in context: A068558 A245058 A240657 * A240662 A188724 A082832
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 22 2015
STATUS
approved