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Number of nX3 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
1

%I #4 Feb 03 2017 08:21:17

%S 4,30,133,587,2559,11251,49293,216274,948407,4159753,18243646,

%T 80014078,350927303,1539109339,6750270615,29605549628,129844926004,

%U 569477896562,2497633716174,10954199079473,48043264384017,210709631957358

%N Number of nX3 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%C Column 3 of A281955.

%H R. H. Hardin, <a href="/A281950/b281950.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +7*a(n-2) -3*a(n-3) -5*a(n-4) +2*a(n-5) +2*a(n-6) -12*a(n-7) +2*a(n-8) -3*a(n-10) for n>12

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281955.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2017