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Number of nX3 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Apr 10 2018 19:28:51

%S 3,9,8,19,42,82,189,469,1029,2372,5661,12788,29440,69193,158299,

%T 364581,849888,1955567,4508226,10463966,24138613,55695301,128985441,

%U 297870624,687700145,1590857932,3675434388,8488858425,19626303139,45350971169

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A302635.

%H R. H. Hardin, <a href="/A302630/b302630.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A302635.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2018