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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)