A233073 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order

1, 2, 2, 5, 9, 5, 14, 50, 50, 14, 41, 289, 582, 289, 41, 122, 1682, 6854, 6854, 1682, 122, 365, 9801, 80811, 164495, 80811, 9801, 365, 1094, 57122, 952869, 3957778, 3957778, 952869, 57122, 1094, 3281, 332929, 11235652, 95264272, 194998895, 95264272

Offset

1,2

Comments

Table starts

....1........2...........5.............14................41

....2........9..........50............289..............1682

....5.......50.........582...........6854.............80811

...14......289........6854.........164495...........3957778

...41.....1682.......80811........3957778.........194998895

..122.....9801......952869.......95264272........9622519979

..365....57122....11235652.....2293174089......475027244071

.1094...332929...132484030....55201144642....23452561697310

.3281..1940450..1562171807..1328800293991..1157902539075279

.9842.11309769.18420188169.31986846738550.57168401542703366

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -7*a(n-2) +a(n-3)

k=3: a(n) = 14*a(n-1) -28*a(n-2) +24*a(n-3) -11*a(n-4) +2*a(n-5) for n>6

k=4: [order 11] for n>12

k=5: [order 21] for n>23

k=6: [order 58] for n>60

Example

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

Crossrefs

Column 1 is A007051(n-1)

Column 2 is A115599

Sequence in context: A011273 A274068 A274065 * A275266 A223387 A278386

Adjacent sequences: A233070 A233071 A233072 * A233074 A233075 A233076

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 03 2013

Status

approved