A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 5, 15, 39, 104, 281, 771, 2122, 5858, 16174, 44694, 123510, 341403, 943694, 2608709, 7211359, 19935055, 55108220, 152341402, 421132682, 1164181573, 3218268552, 8896600238, 24593808939, 67987267220, 187944382019, 519554527901

Offset: 1

Author

R. H. Hardin, Dec 25 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A280069.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3) + 5*a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) for n>9.

Empirical g.f.: x*(1 + x)*(1 - 2*x + 4*x^3 - 8*x^4 + 2*x^5 - x^6 - x^7) / ((1 - x + x^2)*(1 - 2*x - 4*x^2 + 4*x^3 + 3*x^4 + x^5)). - Colin Barker, Feb 12 2019