A281200 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

1, 14, 56, 168, 448, 1120, 2688, 6272, 14336, 32256, 71680, 157696, 344064, 745472, 1605632, 3440640, 7340032, 15597568, 33030144, 69730304, 146800640, 308281344, 645922816, 1350565888, 2818572288, 5872025600, 12213813248, 25367150592

Offset: 1

Author

R. H. Hardin, Jan 17 2017

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..1..0. .0..1..1. .0..0..1. .0..1..0. .0..0..1. .0..0..0. .0..1..1
..1..1..0. .0..1..0. .1..0..1. .0..1..1. .1..1..0. .1..1..0. .1..0..1
..0..1..0. .0..1..0. .1..0..1. .1..0..1. .0..1..0. .0..1..0. .1..0..1
..0..1..0. .0..1..0. .1..1..0. .1..0..0. .0..1..0. .0..1..1. .0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 12.

Crossrefs

Column 3 of A281205.

Formula

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

Conjectures from Colin Barker, Feb 16 2019: (Start)

G.f.: x*(1 + 10*x + 4*x^2) / (1 - 2*x)^2.

a(n) = 7*2^(n-1) * (n-1) for n>1.

(End)