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A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A281051 #8 Feb 15 2019 04:40:42
%S A281051 0,6,68,376,1492,4988,15028,42252,113076,291660,731060,1791052,
%T A281051 4306868,10197068,23828404,55060556,125999028,285894732,643864500,
%U A281051 1440442444,3203438516,7086237772,15599703988,34190878796,74638727092,162339448908
%N A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%H A281051 R. H. Hardin, <a href="/A281051/b281051.txt">Table of n, a(n) for n = 1..210</a>
%F A281051 Empirical: a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 8*a(n-4) for n>6.
%F A281051 Empirical g.f.: 2*x^2*(3 + x)*(1 + 2*x)*(1 + 4*x + 2*x^2) / ((1 + x)*(1 - 2*x)^3). - _Colin Barker_, Feb 15 2019
%e A281051 Some solutions for n=4:
%e A281051 ..0..0..1. .0..1..0. .0..0..0. .0..1..0. .0..1..1. .0..1..0. .0..1..0
%e A281051 ..1..0..0. .0..1..1. .1..0..1. .0..0..1. .0..0..0. .0..1..0. .0..1..0
%e A281051 ..0..1..0. .1..0..0. .1..0..0. .1..1..1. .0..1..1. .1..0..0. .1..0..0
%e A281051 ..0..0..1. .0..1..1. .1..1..0. .1..0..1. .1..0..0. .1..1..1. .1..0..1
%Y A281051 Column 3 of A281056.
%K A281051 nonn
%O A281051 1,2
%A A281051 _R. H. Hardin_, Jan 13 2017