A241349 T(n,k)=Number of nXk 0..3 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..3 introduced in row major order

0, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 22, 36, 22, 3, 6, 103, 415, 415, 103, 6, 11, 519, 4671, 10998, 4671, 519, 11, 23, 2656, 56166, 295782, 295782, 56166, 2656, 23, 47, 13798, 670557, 8216943, 18750240, 8216943, 670557, 13798, 47, 102, 72005, 8072717, 229552661

Offset

1,5

Comments

Table starts

...0......1..........1............2.............3..............6.............11

...1......2..........5...........22...........103............519...........2656

...1......5.........36..........415..........4671..........56166.........670557

...2.....22........415........10998........295782........8216943......229552661

...3....103.......4671.......295782......18750240.....1223251170....80178068077

...6....519......56166......8216943....1223251170...187086636654.28781500332998

..11...2656.....670557....229552661...80178068077.28781500332998

..23..13798....8072717...6440926150.5272889838441

..47..72005...97173041.180941958872

.102.377132.1170969462

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5) for n>6

k=2: [order 10] for n>11

k=3: [order 46] for n>47

Example

Some solutions for n=4 k=4
..0..1..1..1....0..0..1..1....0..0..1..1....0..1..1..1....0..1..2..3
..0..0..0..2....2..1..3..3....2..1..2..2....0..2..0..0....0..1..2..3
..0..2..2..2....2..1..2..2....2..1..0..0....0..2..1..2....2..2..0..3
..3..3..3..2....3..3..1..1....3..3..3..3....3..3..1..2....3..3..0..3

Crossrefs

Column 1 is A199142

Sequence in context: A241555 A277741 A241138 * A330405 A111934 A098509

Adjacent sequences: A241346 A241347 A241348 * A241350 A241351 A241352

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 19 2014

Status

approved