A234029 Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

61, 307, 1543, 7783, 39331, 199003, 1007683, 5105107, 25871611, 131138323, 664800571, 3370454419, 17088658027, 86644639459, 439323545083, 2227578407827, 11294972125867, 57271642785859, 290399314134427, 1472490373513267

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 7*a(n-1) - 6*a(n-2) - 18*a(n-3) - 6*a(n-4).

Empirical g.f.: x*(61 - 120*x - 240*x^2 - 78*x^3) / (1 - 7*x + 6*x^2 + 18*x^3 + 6*x^4). - Colin Barker, Oct 12 2018

Example

Some solutions for n=5:
..4..4....3..4....3..3....4..4....0..1....2..2....3..2....1..2....1..2....1..2
..3..3....3..3....3..3....3..3....0..1....2..1....3..3....2..2....2..2....2..1
..2..2....3..2....4..3....3..3....1..1....1..1....3..2....2..2....3..3....1..1
..1..1....2..3....3..4....2..2....2..1....1..1....3..3....2..1....3..2....1..0
..1..0....3..3....3..4....3..3....2..2....2..1....3..3....1..2....2..2....1..1
..1..0....2..3....3..4....3..4....3..3....1..1....4..3....2..1....2..2....2..1

Crossrefs

Column 1 of A234036.

Sequence in context: A302730 A234036 A142217 * A142923 A154601 A188136

Adjacent sequences: A234026 A234027 A234028 * A234030 A234031 A234032

Keyword

nonn

Author

R. H. Hardin, Dec 18 2013

Status

approved