A230910 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 8, 8, 0, 0, 26, 38, 26, 0, 0, 84, 152, 152, 84, 0, 0, 272, 634, 802, 634, 272, 0, 0, 882, 2676, 4308, 4308, 2676, 882, 0, 0, 2862, 11324, 23614, 30304, 23614, 11324, 2862, 0, 0, 9290, 47954, 130178, 219696, 219696, 130178, 47954, 9290, 0, 0

Offset

1,5

Comments

Table starts

.0....0.....0......0........0.........0..........0...........0.............0

.0....2.....8.....26.......84.......272........882........2862..........9290

.0....8....38....152......634......2676......11324.......47954........203122

.0...26...152....802.....4308.....23614.....130178......718750.......3970738

.0...84...634...4308....30304....219696....1603356....11727974......85870504

.0..272..2676..23614...219696...2121666...20713786...202875672....1989694528

.0..882.11324.130178..1603356..20713786..271505344..3573938648...47146678686

.0.2862.47954.718750.11727974.202875672.3573938648.63341237848.1125893859526

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=2: a(n) = 5*a(n-1) -6*a(n-2) +a(n-3) for n>4

k=3: [order 8] for n>11

k=4: [order 28] for n>31

k=5: [order 89] for n>94

Example

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

Crossrefs

Sequence in context: A091933 A058347 A058547 * A215122 A332473 A235789

Adjacent sequences: A230907 A230908 A230909 * A230911 A230912 A230913

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 01 2013

Status

approved