A233018 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 in row major order

1, 2, 2, 5, 11, 5, 14, 74, 74, 14, 41, 515, 1202, 515, 41, 122, 3602, 19643, 19643, 3602, 122, 365, 25211, 321125, 750092, 321125, 25211, 365, 1094, 176474, 5249894, 28644884, 28644884, 5249894, 176474, 1094, 3281, 1235315, 85827722, 1093911305

Offset

1,2

Comments

Table starts

....1.......2..........5............14...............41.................122

....2......11.........74...........515.............3602...............25211

....5......74.......1202.........19643...........321125.............5249894

...14.....515......19643........750092.........28644884..........1093911305

...41....3602.....321125......28644884.......2555361596........227962456547

..122...25211....5249894....1093911305.....227962456547......47506658438246

..365..176474...85827722...41775098873...20336458202315....9900284810558324

.1094.1235315.1403151863.1595338735322.1814209743962774.2063199965393914025

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -7*a(n-2)

k=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3)

k=4: a(n) = 46*a(n-1) -312*a(n-2) +530*a(n-3) -263*a(n-4)

k=5: [order 8]

k=6: [order 14]

k=7: [order 33]

Example

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

Crossrefs

Column 1 is A007051(n-1)

Column 2 is A199417(n-1)

Sequence in context: A296530 A117400 A005637 * A209100 A208864 A259828

Adjacent sequences: A233015 A233016 A233017 * A233019 A233020 A233021

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 03 2013

Status

approved