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Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Jan 13 2018 11:35:57

%S 3,4,6,18,15,104,227,510,2020,4986,13983,45252,121009,355706,1066100,

%T 2988274,8793219,25704770,73650585,215512322,625817974,1809132934,

%U 5271836919,15292220940,44347166183,128947693186,374125678734

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298154.

%H R. H. Hardin, <a href="/A298149/b298149.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +10*a(n-3) -28*a(n-4) -18*a(n-5) -8*a(n-6) +63*a(n-7) +42*a(n-8) -52*a(n-9) +9*a(n-10) +26*a(n-11) -23*a(n-12) -43*a(n-13) -11*a(n-14) -20*a(n-15) +9*a(n-16) +18*a(n-17) +2*a(n-18) for n>19

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A298154.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 13 2018