A231296 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order.

2, 5, 16, 51, 174, 617, 2223, 8051, 29220, 106109, 385468, 1400401, 5088037, 18486201, 67166528, 244037407, 886670130, 3221565113, 11705027203, 42528259303, 154519400012, 561420537017, 2039828499536, 7411378111905

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) + 16*a(n-4) - 6*a(n-5) - 3*a(n-6) + 4*a(n-8) for n>9.

Empirical g.f.: x*(2 - 3*x - 8*x^2 + 9*x^3 - 14*x^4 + 7*x^5 + 3*x^6 + 4*x^7 + 4*x^8) / ((1 - x)*(1 - x + x^2)*(1 - 2*x - 8*x^2 + 5*x^3 + 8*x^4 + 4*x^5)). - Colin Barker, Sep 28 2018

Example

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

Crossrefs

Column 2 of A231302.

Sequence in context: A148387 A121651 A054660 * A148388 A148389 A108529

Adjacent sequences: A231293 A231294 A231295 * A231297 A231298 A231299

Keyword

nonn

Author

R. H. Hardin, Nov 07 2013

Status

approved