A231445 Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..3 introduced in row major order.

3, 15, 97, 715, 5643, 46075, 382341, 3196783, 26821757, 225400759, 1895576427, 15946759047, 134174450017, 1129009038167, 9500331770337, 79944094951011, 672723905279179, 5660941011339603, 47636625510849789, 400860827109560351

Offset

1,1

Links

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

Formula

Empirical: a(n) = 19*a(n-1) - 133*a(n-2) + 461*a(n-3) - 867*a(n-4) + 881*a(n-5) - 468*a(n-6) + 108*a(n-7).

Empirical g.f.: x*(3 - 42*x + 211*x^2 - 516*x^3 + 645*x^4 - 402*x^5 + 108*x^6) / ((1 - x)*(1 - 5*x + 5*x^2 - 2*x^3)*(1 - 13*x + 45*x^2 - 54*x^3)). - Colin Barker, Sep 29 2018

Example

Some solutions for n=7:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..1....0..0..1....0..1..1....0..0..1....0..0..1....0..0..1....0..0..1
..1..1..1....0..1..0....1..1..2....0..1..1....1..1..0....0..1..0....0..1..2
..0..0..2....1..0..2....1..2..2....0..0..0....0..0..0....1..0..0....1..2..2
..0..2..0....0..2..2....3..3..0....1..1..1....0..0..0....0..0..1....2..3..3
..2..0..2....2..0..0....3..0..0....1..2..2....0..2..2....0..1..1....3..3..2
..0..2..1....0..0..3....2..2..3....2..2..0....2..2..3....1..1..1....2..2..3
..2..1..1....3..3..3....2..3..3....2..0..0....2..3..3....2..2..2....2..3..3

Crossrefs

Column 2 of A231451.

Sequence in context: A370210 A079689 A262751 * A108442 A060148 A143435

Adjacent sequences: A231442 A231443 A231444 * A231446 A231447 A231448

Keyword

nonn

Author

R. H. Hardin, Nov 09 2013

Status

approved