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Number of nX3 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.
1

%I #4 Jan 17 2018 07:52:18

%S 1,12,22,78,283,1097,4503,18491,77067,323638,1361118,5735262,24183115,

%T 102003399,430351949,1815817419,7662005213,32331475024,136431305732,

%U 575712567240,2429399857349,10251633060681,43260101137309

%N Number of nX3 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298328.

%H R. H. Hardin, <a href="/A298323/b298323.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +7*a(n-2) -a(n-3) -23*a(n-4) -16*a(n-5) -17*a(n-6) -85*a(n-7) -11*a(n-8) +187*a(n-9) +53*a(n-10) -118*a(n-11) +5*a(n-12) -24*a(n-13) -87*a(n-14) -25*a(n-15) +28*a(n-16) +16*a(n-17) -2*a(n-18) -a(n-19) for n>20

%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..1..1

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

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

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

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

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

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

%Y Cf. A298328.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 17 2018