A231458 Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order.

7, 8, 15, 20, 32, 56, 111, 230, 501, 1108, 2494, 5646, 12867, 29400, 67363, 154548, 355012, 816044, 1876871, 4318210, 9937849, 22874740, 52659602, 121237426, 279141179, 642732036, 1479959127, 3407837396, 7847200520, 18069880640

Offset

1,1

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) for n>7.

Empirical g.f.: x*(7 - 13*x - 16*x^2 + 16*x^3 + 6*x^4 + 16*x^5 + 12*x^6) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - Colin Barker, Sep 29 2018

Example

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

Crossrefs

Column 2 of A231463.

Sequence in context: A165465 A047521 A231390 * A070424 A022097 A041100

Adjacent sequences: A231455 A231456 A231457 * A231459 A231460 A231461

Keyword

nonn

Author

R. H. Hardin, Nov 09 2013

Status

approved