

A230983


Number of white 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



1, 1, 4, 5, 15, 20, 57, 77, 218, 295, 835, 1130, 3199, 4329, 12256, 16585, 46955, 63540, 179893, 243433, 689202, 932635, 2640455, 3573090, 10116051, 13689141, 38756384, 52445525, 148482575, 200928100, 568863057, 769791157, 2179415178, 2949206335
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OFFSET

1,3


LINKS



FORMULA

Empirical: a(n) = 5*a(n2)  5*a(n4) + 2*a(n6).
Empirical g.f.: x*(1 + x  x^2) / (1  5*x^2 + 5*x^4  2*x^6).  Colin Barker, Sep 25 2018


EXAMPLE

Some solutions for n=6:
..0..x..0....0..x..0....0..x..0....0..x..0....0..x..0....0..x..0....0..x..0
..x..1..x....x..1..x....x..1..x....x..1..x....x..1..x....x..1..x....x..1..x
..0..x..0....0..x..0....0..x..0....1..x..0....0..x..1....1..x..1....0..x..1
..x..0..x....x..0..x....x..1..x....x..0..x....x..0..x....x..0..x....x..0..x
..1..x..1....1..x..1....1..x..1....1..x..0....1..x..0....1..x..0....1..x..1
..x..1..x....x..0..x....x..0..x....x..1..x....x..1..x....x..1..x....x..0..x
..0..x..0....1..x..1....1..x..1....0..x..0....0..x..0....0..x..0....1..x..1


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



