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

Author

R. H. Hardin, Dec 03 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A007051(n-1)

Column 2 is A115599

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