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Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
2

%I #4 Feb 04 2018 13:13:00

%S 4,13,20,27,47,83,137,235,412,709,1228,2150,3758,6578,11556,20330,

%T 35805,63163,111574,197307,349294,618999,1098034,1949511,3464203,

%U 6160917,10965304,19530386,34810655,62087577,110808092,197881858,353585148

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A299187.

%H R. H. Hardin, <a href="/A299182/b299182.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3) -14*a(n-4) +a(n-5) +4*a(n-6) +23*a(n-7) +3*a(n-8) -10*a(n-9) -21*a(n-10) -4*a(n-11) +3*a(n-13) +a(n-14) +6*a(n-15) +6*a(n-16) +4*a(n-17) for n>19

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A299187.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2018