A239150 Number of (n+1) X (1+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

1, 1, 7, 17, 96, 340, 1639, 6623, 29843, 126163, 554310, 2380524, 10363965, 44756085, 194216303, 840357677, 3642433780, 15771490916, 68331367227, 295943443667, 1282011757819, 5552887116543, 24053558944522, 104188496250108

Offset

1,3

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 7*a(n-2) - 26*a(n-3) + 5*a(n-4) + 14*a(n-5).

Empirical g.f.: x*(1 - 3*x - 4*x^2 + 8*x^3) / ((1 - x - x^2)*(1 - 3*x - 9*x^2 + 14*x^3)).

Example

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

Crossrefs

Column 1 of A239155.

Sequence in context: A359015 A177123 A124165 * A092057 A082738 A092340

Adjacent sequences: A239147 A239148 A239149 * A239151 A239152 A239153

Keyword

nonn

Author

R. H. Hardin, Mar 11 2014

Status

approved