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Number of 3Xn 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Mar 27 2018 10:14:32

%S 0,5,4,25,74,278,968,3450,12210,43316,153582,544554,1930920,6846494,

%T 24276442,86078740,305217538,1082235538,3837379072,13606528258,

%U 48245865110,171069584080,606576433502,2150791206274,7626248942608

%N Number of 3Xn 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

%C Row 3 of A301823.

%H R. H. Hardin, <a href="/A301824/b301824.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +6*a(n-2) -a(n-3) -3*a(n-4) +4*a(n-5) -4*a(n-6) -32*a(n-7) -9*a(n-8) -4*a(n-9) -19*a(n-10) +17*a(n-11) +3*a(n-12) +a(n-13) -a(n-14) for n>18

%e Some solutions for n=5

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

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

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

%Y Cf. A301823.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 27 2018