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

%I #4 Mar 04 2018 09:16:23

%S 1,2,4,11,8,58,131,306,936,2435,6683,18093,49663,134666,367314,

%T 1002020,2728817,7439403,20275261,55264984,150614904,410527337,

%U 1118909399,3049617734,8311952136,22654640136,61746476769,168293237171,458692748831

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

%C Column 3 of A300380.

%H R. H. Hardin, <a href="/A300375/b300375.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-2) +9*a(n-3) +9*a(n-4) +3*a(n-5) -8*a(n-6) -a(n-7) -18*a(n-8) -24*a(n-9) -45*a(n-10) -10*a(n-11) -15*a(n-12) +39*a(n-13) -21*a(n-14) +9*a(n-15) -7*a(n-16) -13*a(n-17) +14*a(n-18) -5*a(n-19) +3*a(n-20) -2*a(n-22) +a(n-23) for n>25

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300380.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 04 2018