A231747 Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

3, 15, 51, 186, 687, 2485, 9068, 33308, 121445, 444183, 1626731, 5949198, 21774916, 79713938, 291767058, 1068145321, 3910543065, 14316731138, 52417430039, 191916565888, 702674552025, 2572785049162, 9420099176524, 34491356066515

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 14*a(n-3) - 39*a(n-4) - 45*a(n-5) - 124*a(n-6) + 18*a(n-7) + 132*a(n-8) + 248*a(n-9) + 112*a(n-10) + 64*a(n-11).

Empirical g.f.: x*(3 + 6*x - 3*x^2 - 54*x^3 - 117*x^4 - 128*x^5 - 16*x^6 + 386*x^7 + 348*x^8 + 224*x^9 + 64*x^10) / (1 - 3*x - 3*x^2 - 14*x^3 + 39*x^4 + 45*x^5 + 124*x^6 - 18*x^7 - 132*x^8 - 248*x^9 - 112*x^10 - 64*x^11). - Colin Barker, Sep 30 2018

Example

Some solutions for n=7:
..1..0....2..2....0..2....0..0....1..0....2..1....0..0....0..0....2..0....0..2
..0..0....1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....1..1....0..0....0..0....0..0....0..0....0..1....1..2....0..0....0..0
..0..0....1..1....2..1....1..1....0..0....0..0....0..0....1..1....0..2....0..1
..1..2....2..1....0..0....2..1....1..1....0..0....0..0....1..2....0..0....0..2
..1..1....2..1....0..0....1..1....1..1....2..0....2..1....1..1....0..0....0..0
..1..1....1..1....1..0....1..2....1..1....0..0....1..1....1..2....0..2....0..2

Crossrefs

Column 2 of A231753.

Sequence in context: A118126 A282464 A284663 * A192742 A166035 A038192

Adjacent sequences: A231744 A231745 A231746 * A231748 A231749 A231750

Keyword

nonn

Author

R. H. Hardin, Nov 13 2013

Status

approved