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A223062
T(n,k)=Number of nXk 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order
8
1, 2, 2, 5, 10, 5, 15, 114, 114, 15, 51, 1473, 4865, 1473, 51, 187, 19360, 213469, 213469, 19360, 187, 715, 255045, 9383963, 31331820, 9383963, 255045, 715, 2795, 3361024, 412602889, 4606719559, 4606719559, 412602889, 3361024, 2795, 11051, 44294253
OFFSET
1,2
COMMENTS
Table starts
...1......2.........5...........15...............51.................187
...2.....10.......114.........1473............19360..............255045
...5....114......4865.......213469..........9383963...........412602889
..15...1473....213469.....31331820.......4606719559........677531592132
..51..19360...9383963...4606719559....2266567594841....1115636153544055
.187.255045.412602889.677531592132.1115636153544055.1837966217755803448
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
k=2: a(n) = 18*a(n-1) -71*a(n-2) +102*a(n-3) -48*a(n-4) for n>5
k=3: a(n) = 55*a(n-1) -515*a(n-2) +1337*a(n-3) -696*a(n-4) -1188*a(n-5) +1008*a(n-6) for n>7
k=4: [order 11 for n>12]
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..1....0..1..1..0
..2..2..0..1....2..1..0..2....2..3..0..2....2..1..2..2....0..2..3..0
..3..3..3..3....2..3..1..0....2..1..2..0....3..2..3..0....0..2..0..1
CROSSREFS
Column 1 is A007581(n-1)
Sequence in context: A208567 A273968 A273964 * A208788 A246864 A262924
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 13 2013
STATUS
approved