A231221 Number of (n+2) X (2+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

2, 4, 8, 17, 45, 103, 264, 676, 1724, 4501, 11679, 30579, 80180, 210494, 553858, 1457853, 3840945, 10124071, 26693522, 70402100, 185706800, 489925347, 1292616577, 3410640207, 8999588762, 23747752874, 62666069376, 165367179091

Offset: 1

Author

R. H. Hardin, Nov 05 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A231227.

Formula

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 6*a(n-3) - 7*a(n-4) + 5*a(n-5) - a(n-6) + 6*a(n-7) + 17*a(n-8) - 20*a(n-9) - 2*a(n-10) + 4*a(n-11).

Empirical g.f.: x*(2 - 2*x - 8*x^2 - 3*x^3 + 16*x^4 + 5*x^6 + 19*x^7 - 34*x^8 - 2*x^9 + 8*x^10) / ((1 - x)*(1 - 2*x - 4*x^2 + 2*x^3 + 9*x^4 + 4*x^5 + 5*x^6 - x^7 - 18*x^8 + 2*x^9 + 4*x^10)). - Colin Barker, Sep 27 2018