login
Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
1

%I #4 Jul 15 2018 14:10:17

%S 4,14,37,105,388,1280,4121,13933,46641,154593,516270,1725502,5753200,

%T 19197252,64095188,213911810,713904833,2382943651,7953695202,

%U 26546786860,88606850547,295748963969,987132925969,3294803783913,10997255560702

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A316883.

%H R. H. Hardin, <a href="/A316878/b316878.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +14*a(n-3) -19*a(n-4) -63*a(n-5) -93*a(n-6) +71*a(n-7) +279*a(n-8) +285*a(n-9) -86*a(n-10) -418*a(n-11) -276*a(n-12) +28*a(n-13) +90*a(n-14) -9*a(n-15) for n>17

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A316883.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 15 2018