A229372 T(n,k)=Number of nXk 0..2 arrays avoiding 11 horizontally, 22 vertically and 00 antidiagonally

3, 8, 8, 22, 38, 22, 60, 184, 184, 60, 164, 869, 1610, 869, 164, 448, 4144, 13937, 13937, 4144, 448, 1224, 19675, 122497, 222990, 122497, 19675, 1224, 3344, 93589, 1067299, 3576912, 3576912, 1067299, 93589, 3344, 9136, 444824, 9346997, 56939585

Offset

1,1

Comments

Table starts

....3......8.......22..........60...........164.............448

....8.....38......184.........869..........4144...........19675

...22....184.....1610.......13937........122497.........1067299

...60....869....13937......222990.......3576912........56939585

..164...4144...122497.....3576912.....104382552......3043629267

..448..19675..1067299....56939585....3043629267....162794962814

.1224..93589..9346997...911301584...89084628843...8710922742428

.3344.444824.81633583.14532090528.2599351293506.465220677212678

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +2*a(n-2)

k=2: a(n) = 2*a(n-1) +13*a(n-2) +3*a(n-3) -13*a(n-4) +4*a(n-5)

k=3: [order 11]

k=4: [order 24] for n>25

k=5: [order 50] for n>54

Example

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

Crossrefs

Column 1 is A028859

Sequence in context: A101385 A161432 A229380 * A357406 A021261 A245263

Adjacent sequences: A229369 A229370 A229371 * A229373 A229374 A229375

Keyword

nonn,tabl

Author

R. H. Hardin Sep 21 2013

Status

approved