reviewed

approved

proposed

reviewed

editing

proposed

Number of nX3 n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

Column 3 of A268639.

Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).

Empirical g.f.: 6*x*(2 - 2*x^2 + 3*x^3) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 14 2019

Some solutions for n=6:

Cf. Column 3 of A268639.

approved

editing

editing

approved

R. H. Hardin, <a href="/A268634/b268634.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

12, 120, 840, 5178, 29772, 163878, 875592, 4578186, 23548164, 119570574, 600870336, 2993807250, 14810051580, 72819229974, 356173467576, 1734202809114, 8410141924596, 40641730213278, 195782548631472, 940481337385122

1,1

Column 3 of A268639.

Empirical: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4)

Some solutions for n=6

..0..0..0. .1..0..0. .1..0..0. .2..1..0. .0..1..2. .1..0..1. .1..0..0

..0..1..1. .0..1..0. .2..1..0. .1..0..0. .1..2..1. .0..1..0. .2..2..1

..0..0..0. .1..2..1. .1..0..0. .2..1..0. .2..2..1. .1..0..0. .2..1..0

..0..0..1. .2..2..2. .2..1..1. .2..0..0. .2..1..0. .2..1..0. .1..2..1

..0..1..0. .2..1..2. .1..2..2. .1..0..1. .1..2..1. .0..0..0. .2..2..2

..1..0..0. .0..0..1. .2..2..2. .2..1..0. .0..1..2. .0..0..0. .1..2..2

Cf. A268639.

allocated

nonn

R. H. Hardin, Feb 09 2016

approved

editing

allocated for R. H. Hardin

allocated

approved