A262332 T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

2, 3, 3, 6, 5, 6, 11, 15, 15, 11, 22, 33, 90, 33, 22, 43, 99, 351, 351, 99, 43, 86, 261, 2106, 2399, 2106, 261, 86, 171, 783, 10935, 26131, 26131, 10935, 783, 171, 342, 2241, 65610, 252097, 570922, 252097, 65610, 2241, 342, 683, 6723, 378351, 2767631, 10789339

Offset

1,1

Comments

Table starts

...2.....3........6.........11............22...............43

...3.....5.......15.........33............99..............261

...6....15.......90........351..........2106............10935

..11....33......351.......2399.........26131...........252097

..22....99.....2106......26131........570922.........10789339

..43...261....10935.....252097......10789339........394241389

..86...783....65610....2767631.....237172426......16940254423

.171..2241...378351...29452071....5028462531.....699094613961

.342..6723..2270106..323841891..110616890922...30056993215803

.683.19845.13482855.3532758473.2411745951979.1279198648576981

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

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 15]

k=7: [order 19]

Example

Some solutions for n=4, k=4
..0..0..0..0..0....0..1..1..1..1....1..1..0..1..1....0..0..0..1..1
..1..1..1..1..0....1..1..0..0..0....1..0..1..0..1....1..1..0..1..1
..1..1..1..1..0....1..1..1..1..0....1..0..0..1..0....1..0..0..1..0
..1..1..0..0..0....0..1..0..0..1....1..1..0..0..0....0..0..0..1..1
..1..1..0..0..0....0..0..1..1..0....0..0..1..1..0....0..1..0..0..1

Crossrefs

Column 1 is A005578(n+1).

Sequence in context: A014498 A186286 A023821 * A262240 A333660 A187754

Adjacent sequences: A262329 A262330 A262331 * A262333 A262334 A262335

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 18 2015

Status

approved