A231221 - OEIS

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

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OFFSET

1,1

LINKS

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

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

EXAMPLE

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

..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

CROSSREFS

Column 2 of A231227.

Sequence in context: A367114 A283162 A364210 * A231435 A113153 A372543

Adjacent sequences: A231218 A231219 A231220 * A231222 A231223 A231224

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 05 2013

STATUS

approved