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Number of 3Xn 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
1

%I #4 Mar 15 2017 08:05:11

%S 0,6,159,1088,7839,56106,369328,2391828,15258307,95588636,592291968,

%T 3636441278,22144892123,133969251618,805895076555,4824002960360,

%U 28752431241931,170726461743312,1010344566340239,5961242307456936

%N Number of 3Xn 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%C Row 3 of A283726.

%H R. H. Hardin, <a href="/A283728/b283728.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -19*a(n-2) -303*a(n-4) +588*a(n-5) +507*a(n-6) +2028*a(n-7) -5758*a(n-8) -5310*a(n-9) +4331*a(n-10) +15486*a(n-11) +7169*a(n-12) -26070*a(n-13) -7596*a(n-14) +7938*a(n-15) +16823*a(n-16) -5350*a(n-17) -11837*a(n-18) +11864*a(n-19) -5720*a(n-20) +1400*a(n-21) -196*a(n-22)

%e Some solutions for n=4

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

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

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

%Y Cf. A283726.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 15 2017