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Number of nX2 n X 2 0..1 arrays with no element equal to more than two horizontal or vertical neighbors, with new values 0..1 introduced in row major order.

Column 2 of A240484.

Empirical: a(n) = 3*a(n-1) + a(n-2) - 2*a(n-4).

Empirical g.f.: x*(2 + 2*x - x^2 - 2*x^3) / (1 - 3*x - x^2 + 2*x^4). - Colin Barker, Feb 24 2018

Some solutions for n=4:

Cf. A240484.

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R. H. Hardin, <a href="/A240478/b240478.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX2 0..1 arrays with no element equal to more than two horizontal or vertical neighbors, with new values 0..1 introduced in row major order

2, 8, 25, 81, 264, 857, 2785, 9050, 29407, 95557, 310508, 1008981, 3278637, 10653778, 34618955, 112492681, 365539724, 1187804297, 3859714705, 12541963050, 40754524407, 132429927677, 430324878028, 1398320635661, 4543777736197

1,1

Column 2 of A240484

Empirical: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)

Some solutions for n=4

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

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

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

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

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nonn

R. H. Hardin, Apr 06 2014

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