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Number of n X 2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.
2

%I #8 Nov 16 2021 21:42:13

%S 0,4,16,68,256,924,3232,11044,37104,122984,403280,1310760,4228960,

%T 13558932,43239776,137251068,433883696,1366668772,4290998336,

%U 13433966724,41949331616,130685405648,406258440928,1260465716560,3903760205760

%N Number of n X 2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

%C Column 2 of A283042.

%H R. H. Hardin, <a href="/A283036/b283036.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8).

%F Empirical: G.f.: -4*x^2*(x-1)*(1+x)/(x^4-3*x^2-2*x+1)^2. - _R. J. Mathar_, Mar 02 2017

%e Some solutions for n=4

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

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

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

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

%Y Cf. A283042.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 27 2017