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R. H. Hardin, <a href="/A297336/b297336.txt">Table of n, a(n) for n = 1..210</a>

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Number of nX6 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.

21, 333, 4888, 73147, 1091456, 16277492, 242728633, 3619361855, 53967869192, 804703360025, 11998734637184, 178910069329084, 2667681781924513, 39777110424677008, 593106152583574704, 8843651586637481947

1,1

Column 6 of A297338.

Empirical: a(n) = 24*a(n-1) -154*a(n-2) +246*a(n-3) +521*a(n-4) -1157*a(n-5) -1119*a(n-6) +1776*a(n-7) +1209*a(n-8) -621*a(n-9) -454*a(n-10) -25*a(n-11) +10*a(n-12) +a(n-13) for n>14

Some solutions for n=5

..0..0..1..0..0..0. .0..0..0..1..0..0. .0..0..0..1..0..0. .0..0..0..1..0..0

..0..0..1..0..0..1. .1..0..0..1..0..0. .0..1..0..0..0..0. .1..0..0..0..0..0

..0..0..0..0..0..1. .0..0..0..1..1..0. .0..1..0..1..0..1. .0..0..0..0..1..0

..0..0..1..0..0..0. .0..0..1..1..0..0. .0..0..0..1..0..0. .0..0..1..0..0..1

..0..0..0..0..0..1. .0..0..0..0..0..0. .0..0..0..1..0..1. .0..0..0..1..0..0

Cf. A297338.

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R. H. Hardin, Dec 28 2017

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