A231703 Number of (n+1) X (1+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to one.

5, 17, 42, 121, 351, 978, 2768, 7851, 22168, 62688, 177333, 501398, 1417871, 4009693, 11338691, 32064185, 90673442, 256411571, 725096165, 2050472356, 5798450868, 16397214669, 46369052496, 131125251872, 370804035439, 1048582421408

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) + 4*a(n-3) - 8*a(n-4) + 3*a(n-5) - 3*a(n-6) + 3*a(n-7) - 2*a(n-8) + a(n-9).

Empirical g.f.: x*(5 + 2*x - 4*x^2 - 8*x^3 + 2*x^4 - x^5 + x^6 - x^7 + x^8) / (1 - 3*x + x^2 - 4*x^3 + 8*x^4 - 3*x^5 + 3*x^6 - 3*x^7 + 2*x^8 - x^9). - Colin Barker, Sep 30 2018

Example

Some solutions for n=7:
..1..1....0..1....0..0....0..1....0..0....0..0....0..0....0..0....1..1....0..1
..0..0....0..0....0..0....0..0....0..0....1..0....0..1....0..1....0..0....0..0
..0..0....1..0....1..1....0..1....1..0....1..0....0..0....1..1....0..0....0..1
..0..1....1..0....0..0....0..0....0..1....0..0....1..0....0..0....1..0....0..0
..1..0....0..0....0..0....0..1....0..0....1..1....0..0....0..0....0..1....0..1
..0..0....1..0....0..0....0..1....1..0....1..0....1..0....0..0....0..0....0..0
..0..0....1..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....1..0
..0..0....1..0....0..1....0..0....1..1....1..0....0..1....0..1....0..0....0..0

Crossrefs

Column 1 of A231710.

Sequence in context: A111746 A088645 A055609 * A265193 A146720 A146640

Adjacent sequences: A231700 A231701 A231702 * A231704 A231705 A231706

Keyword

nonn

Author

R. H. Hardin, Nov 12 2013

Status

approved