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Number of nX3 0..1 arrays with every element equal to 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
1

%I #4 Jan 21 2018 06:08:42

%S 1,17,109,588,3276,18500,104034,585134,3291766,18516878,104162234,

%T 585942186,3296084046,18541374458,104300314322,586717825798,

%U 3300448449034,18565926430146,104438420710534,587494718619882

%N Number of nX3 0..1 arrays with every element equal to 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298547.

%H R. H. Hardin, <a href="/A298542/b298542.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +3*a(n-2) +6*a(n-3) -15*a(n-4) -11*a(n-5) -5*a(n-6) -46*a(n-7) -2*a(n-8) -38*a(n-9) -16*a(n-10) -8*a(n-11) -8*a(n-12) for n>13

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A298547.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 21 2018