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Number of nX3 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
1

%I #4 May 22 2018 11:23:12

%S 1,16,42,118,371,1203,3917,12919,42060,137964,453179,1485554,4873627,

%T 15999482,52491249,172244821,565295892,1855010713,6087300807,

%U 19976720519,65555588200,215127264249,705970664448,2316727402348,7602611158078

%N Number of nX3 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A304959.

%H R. H. Hardin, <a href="/A304954/b304954.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +8*a(n-3) -12*a(n-4) -42*a(n-5) +3*a(n-6) +a(n-7) +30*a(n-8) +58*a(n-9) +60*a(n-10) +18*a(n-11) -90*a(n-12) -70*a(n-13) -48*a(n-14) +30*a(n-15) +39*a(n-16) +2*a(n-17) +4*a(n-18) -4*a(n-19) -4*a(n-20) for n>21

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304959.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 22 2018