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.

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

Author

R. H. Hardin Mar 13 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A007581(n-1)

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]