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A232335
T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal
12
1, 2, 1, 4, 6, 1, 6, 18, 16, 1, 10, 32, 74, 42, 1, 16, 82, 154, 308, 110, 1, 26, 162, 628, 734, 1282, 288, 1, 42, 388, 1470, 4906, 3472, 5338, 754, 1, 68, 806, 5530, 13170, 38986, 16338, 22228, 1974, 1, 110, 1858, 13906, 82526, 117690, 312276, 76630, 92562, 5168
OFFSET
1,2
COMMENTS
Table starts
.1.....2.......4.......6.........10.........16............26............42
.1.....6......18......32.........82........162...........388...........806
.1....16......74.....154........628.......1470..........5530.........13906
.1....42.....308.....734.......4906......13170.........82526........239992
.1...110....1282....3472......38986.....117690.......1274656.......4158066
.1...288....5338...16338.....312276....1047700......20052758......71916112
.1...754...22228...76630....2510674....9298730.....318521414....1241196022
.1..1974...92562..358656...20221026...82332898....5084744564...21383016966
.1..5168..385450.1676330..162993780..727588212...81376107850..367791626696
.1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)
k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)
k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5
k=6: [order 7] for n>9
k=7: [order 16] for n>18
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6
n=3: [order 8] for n>12
n=4: [order 21] for n>24
n=5: [order 36] for n>42
n=6: [order 80] for n>87
EXAMPLE
Some solutions for n=5 k=4
..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1
..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1
..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2
..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2
..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..2
CROSSREFS
Column 2 is A025169(n-1)
Column 3 is A218059
Row 1 is A006355(n+1)
Sequence in context: A369518 A199530 A208765 * A098473 A121757 A219441
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 22 2013
STATUS
approved