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

1,1

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

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

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

Adjacent sequences: A262417 A262418 A262419 * A262421 A262422 A262423

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 22 2015

Status

approved