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

%I #4 Jun 25 2018 17:36:48

%S 1,11,16,34,113,275,604,1804,4683,11365,31038,82942,210403,558769,

%T 1491058,3874324,10204095,27097133,71126798,187171924,495234515,

%U 1304838307,3436483078,9075524470,23939196931,63097831781,166506104866

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

%C Column 3 of A316176.

%H R. H. Hardin, <a href="/A316171/b316171.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +3*a(n-2) +16*a(n-3) -7*a(n-4) -48*a(n-5) -97*a(n-6) -a(n-7) +213*a(n-8) +247*a(n-9) +83*a(n-10) -282*a(n-11) -215*a(n-12) +10*a(n-13) +105*a(n-14) -81*a(n-15) -80*a(n-16) -38*a(n-17) -4*a(n-18) for n>20

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A316176.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 25 2018