A281050 - OEIS

A281050

Number of n X 2 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 #8 Feb 15 2019 04:40:39

%S 0,1,6,29,122,468,1686,5807,19338,62731,199264,622152,1914780,5821645,

%T 17515566,52221929,154461110,453654108,1324053522,3842768987,

%U 11096398578,31895230903,91296545404,260329675536,739725018360,2095147333465

%N Number of n X 2 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 R. H. Hardin, <a href="/A281050/b281050.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 30*a(n-2) + 45*a(n-3) - 30*a(n-4) + 9*a(n-5) - a(n-6).

%F Empirical g.f.: x^2*(1 - 3*x + 5*x^2 - 4*x^3) / (1 - 3*x + x^2)^3. - _Colin Barker_, Feb 15 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A281056.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 13 2017