A231126 - OEIS

%I #7 Mar 18 2018 06:22:59

%S 6,40,308,2260,16812,124644,924900,6862052,50913012,377747700,

%T 2802692276,20794524084,154284599124,1144711823796,8493168927828,

%U 63014915159220,467538037568404,3468890119531892,25737368287958996,190957944347003188

%N Number of (n+1) X (3+1) white-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%C Column 3 of A231131.

%H R. H. Hardin, <a href="/A231126/b231126.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) + 8*a(n-2) - 32*a(n-3) - 38*a(n-4) + 40*a(n-5) + 56*a(n-6) - 16*a(n-7) - 16*a(n-8).

%F Empirical g.f.: 2*x*(3 - x - 10*x^2 - 12*x^3 + 18*x^4 + 8*x^5 - 8*x^6) / (1 - 7*x - 8*x^2 + 32*x^3 + 38*x^4 - 40*x^5 - 56*x^6 + 16*x^7 + 16*x^8). - _Colin Barker_, Mar 18 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Cf. A231131.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 04 2013