A231337 Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.

3, 4, 7, 12, 24, 48, 103, 222, 493, 1100, 2486, 5638, 12859, 29392, 67355, 154540, 355004, 816036, 1876863, 4318202, 9937841, 22874732, 52659594, 121237418, 279141171, 642732028, 1479959119, 3407837388, 7847200512, 18069880632

Offset

1,1

Comments

Column 1 of A231343.

Links

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

Formula

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

Empirical g.f.: x*(3 - 5*x - 8*x^2 + 8*x^3 + 6*x^4) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - Colin Barker, Feb 24 2018

Example

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

Crossrefs

Cf. A231343.

Sequence in context: A062202 A049859 A124636 * A049930 A102938 A076784

Adjacent sequences: A231334 A231335 A231336 * A231338 A231339 A231340

Keyword

nonn

Author

R. H. Hardin, Nov 07 2013

Status

approved