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Number of nX3 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
1

%I #4 Jan 12 2018 08:59:05

%S 0,3,0,3,1,7,18,52,144,405,1124,3113,8688,24346,68385,192524,542537,

%T 1529960,4316175,12178973,34370746,97008377,273813995,772895361,

%U 2181712563,6158599574,17384869895,49075425772,138534755824,391070202040

%N Number of nX3 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298087.

%H R. H. Hardin, <a href="/A298082/b298082.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3) -11*a(n-4) +a(n-5) +15*a(n-6) +7*a(n-7) +a(n-8) -24*a(n-9) -39*a(n-10) +13*a(n-11) +32*a(n-12) +8*a(n-13) +5*a(n-14) -2*a(n-15) -2*a(n-16) for n>17

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A298087.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 12 2018