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

1,2

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.

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)

Example

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

Crossrefs

Column 3 of A281205.

Sequence in context: A192846 A212347 A115129 * A212341 A067326 A202242

Adjacent sequences: A281197 A281198 A281199 * A281201 A281202 A281203

Keyword

nonn

Author

R. H. Hardin, Jan 17 2017

Status

approved