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.

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

Author

R. H. Hardin, Sep 22 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..240

Crossrefs

Column 1 is A000975(n+1).

Row 1 is A047849((n+1)/2) for odd n.

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]