A283951 - OEIS

A283951

Number of 2Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%I #6 Mar 21 2017 23:19:50

%S 0,0,2,16,84,408,1926,8776,38912,169456,727914,3091712,13010668,

%T 54334792,225449486,930278584,3820249240,15622389664,63649588850,

%U 258473068912,1046543827972,4226200851704,17025631341974,68440231400232

%N Number of 2Xn 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%C Row 2 of A283950.

%H R. H. Hardin, <a href="/A283951/b283951.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) -7*a(n-2) +8*a(n-3) -31*a(n-4) -50*a(n-5) -61*a(n-6) -84*a(n-7) -36*a(n-8).

%F Empirical g.f.: G.f.: 2*x^3*(1+x)^2/(-1+3*x+x^2+7*x^3+6*x^4)^2 . - _R. J. Mathar_, Mar 21 2017

%e Some solutions for n=4

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

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

%Y Cf. A283950.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 18 2017