A233026 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

1, 3, 3, 9, 15, 9, 27, 81, 81, 27, 81, 435, 849, 435, 81, 243, 2337, 8835, 8835, 2337, 243, 729, 12555, 92067, 179999, 92067, 12555, 729, 2187, 67449, 959385, 3685017, 3685017, 959385, 67449, 2187, 6561, 362355, 9997413, 75489671, 149128385

Offset: 1

Author

R. H. Hardin, Dec 03 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....1........3...........9.............27................81

.....3.......15..........81............435..............2337

.....9.......81.........849...........8835.............92067

....27......435........8835.........179999...........3685017

....81.....2337.......92067........3685017.........149128385

...243....12555......959385.......75489671........6050598339

...729....67449.....9997413.....1546718177......245698677999

..2187...362355...104179551....31692006853.....9979662714381

..6561..1946673..1085618895...649369155341...405380056659145

.19683.10458075.11312857317.13305594622397.16467175046293207

Examples

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

Links

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

Crossrefs

Column 1 is A000244(n-1)

Formula

Empirical for column k:

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

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

k=3: a(n) = 11*a(n-1) -5*a(n-2) -11*a(n-3) +2*a(n-4)

k=4: [order 8]

k=5: [order 20]

k=6: [order 50]