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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000244(n-1)

Sequence in context: A197462 A264098 A223209 * A105423 A147471 A062510

Adjacent sequences: A233023 A233024 A233025 * A233027 A233028 A233029

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 03 2013

Status

approved