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Number of nX4 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
1

%I #4 Jan 20 2017 14:11:56

%S 8,85,193,607,1892,5868,18189,56154,173062,534110,1650156,5098879,

%T 15751692,48653245,150278118,464200703,1433942077,4429534747,

%U 13682972108,42266936805,130563482897,403314526070,1245852260586,3848479634326

%N Number of nX4 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%C Column 4 of A281344.

%H R. H. Hardin, <a href="/A281340/b281340.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3) -a(n-5) -8*a(n-6) -35*a(n-7) +29*a(n-8) +32*a(n-9) +39*a(n-10) -35*a(n-11) -31*a(n-12) +5*a(n-13) +14*a(n-14) -3*a(n-15) -14*a(n-16) +2*a(n-17) +4*a(n-18) for n>21

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281344.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2017