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.

%I #7 Sep 27 2018 15:31:46

%S 2,4,8,17,45,103,264,676,1724,4501,11679,30579,80180,210494,553858,

%T 1457853,3840945,10124071,26693522,70402100,185706800,489925347,

%U 1292616577,3410640207,8999588762,23747752874,62666069376,165367179091

%N 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.

%H R. H. Hardin, <a href="/A231221/b231221.txt">Table of n, a(n) for n = 1..210</a>

%F 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).

%F 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

%e Some solutions for n=5:

%e ..0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0

%e ..1..1..0..0....0..0..1..1....0..0..1..1....0..0..1..1....1..1..1..1

%e ..1..1..0..0....1..1..1..1....1..1..0..0....1..1..1..1....1..1..1..1

%e ..1..1..0..0....1..1..0..0....1..1..0..0....1..1..2..2....1..1..1..1

%e ..0..0..1..1....0..0..0..0....1..1..0..0....2..2..2..2....0..0..0..0

%Y Column 2 of A231227.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 05 2013