A231067 Number of black square subarrays of (n+1) X (2+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.

1, 3, 4, 11, 15, 42, 57, 161, 218, 617, 835, 2364, 3199, 9057, 12256, 34699, 46955, 132938, 179893, 509309, 689202, 1951253, 2640455, 7475596, 10116051, 28640333, 38756384, 109726191, 148482575, 420380482, 568863057, 1610552121, 2179415178

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-2) - 5*a(n-4) + 2*a(n-6).

Empirical g.f.: x*(1 + 3*x - x^2 - 4*x^3 + 2*x^5) / (1 - 5*x^2 + 5*x^4 - 2*x^6). - Colin Barker, Sep 26 2018

Example

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

Crossrefs

Column 2 of A231070.

Sequence in context: A042483 A002530 A042709 * A042327 A046114 A116654

Adjacent sequences: A231064 A231065 A231066 * A231068 A231069 A231070

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved