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Number of nX3 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Apr 06 2018 12:17:34

%S 1,12,31,109,397,1430,5110,18395,66203,238103,856413,3081033,11083994,

%T 39873749,143444250,516038048,1856433397,6678469130,24025629692,

%U 86431623758,310935653685,1118583441105,4024076800534,14476518656548

%N Number of nX3 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A302367.

%H R. H. Hardin, <a href="/A302362/b302362.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -3*a(n-2) +9*a(n-3) -9*a(n-4) -11*a(n-5) +a(n-6) -18*a(n-7) +16*a(n-8) -12*a(n-9) -4*a(n-10) +4*a(n-11) +8*a(n-12)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A302367.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 06 2018