A268967 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

60, 912, 11664, 136080, 1504656, 16061328, 167226768, 1709114256, 17218688400, 171498136464, 1692252695952, 16569199473552, 161173122151824, 1559011041375120, 15007175850454416, 143849270956794768

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

Conjectures from Colin Barker, Jan 17 2019: (Start)

G.f.: 12*x*(1 - x)*(5 - 9*x) / (1 - 9*x)^2.

a(n) = 16*3^(2*n-3) * (8*n+3) for n>1.

(End)

Example

Some solutions for n=4:
..1..0..0..0. .1..0..1..2. .2..1..0..1. .2..1..2..1. .2..1..2..1
..1..0..0..1. .0..0..1..2. .0..0..0..0. .2..1..2..2. .2..1..2..2
..0..1..2..0. .1..0..2..2. .1..2..1..2. .2..2..1..2. .0..0..1..2
..2..1..0..0. .0..1..2..1. .1..0..1..0. .1..0..1..1. .1..2..1..2

Crossrefs

Column 4 of A268971.

Sequence in context: A305625 A056321 A056312 * A189607 A223213 A271651

Adjacent sequences: A268964 A268965 A268966 * A268968 A268969 A268970

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved