A281209 - OEIS

%I #7 Feb 18 2019 08:16:31

%S 0,130,448,676,1141,1906,3137,5160,8510,14084,23379,38894,64795,

%T 108022,180126,300318,500525,833770,1388053,2309332,3839550,6379528,

%U 10592935,17578086,29151695,48317346,80038622,132514530,219282785,362687074

%N Number of 5 X n 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281209/b281209.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>11.

%F Empirical g.f.: x^2*(130 - 72*x - 596*x^2 + 489*x^3 + 422*x^4 - 363*x^5 - 56*x^6 + 114*x^7 + 10*x^8 - 4*x^9) / ((1 - x)^2*(1 - x - x^2)^2). - _Colin Barker_, Feb 18 2019

%e Some solutions for n=4:

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

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

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

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

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

%Y Row 5 of A281205.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 17 2017