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Number of nX3 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Apr 20 2018 10:52:00

%S 1,11,18,55,181,494,1465,4415,12934,38423,114145,337914,1003161,

%T 2976083,8824906,26185191,77678573,230413110,683562697,2027805127,

%U 6015399582,17845009895,52937661977,157040038306,465863595657,1381994981979

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

%C Column 3 of A303242.

%H R. H. Hardin, <a href="/A303237/b303237.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -5*a(n-2) +16*a(n-3) -36*a(n-4) +32*a(n-5) -63*a(n-6) +64*a(n-7) -51*a(n-8) +4*a(n-9) +60*a(n-10) +16*a(n-11) +112*a(n-12) +64*a(n-13)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A303242.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 20 2018