A281208 Number of 4 X n 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.

0, 38, 168, 270, 470, 804, 1358, 2284, 3834, 6432, 10786, 18080, 30290, 50712, 84838, 141812, 236846, 395228, 658966, 1097796, 1827410, 3039624, 5052282, 8391768, 13929370, 23106544, 38306878, 63470044, 105104774, 173959572, 287777246

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6) for n>10.

Empirical g.f.: 2*x^2*(19 + 8*x - 125*x^2 + 69*x^3 + 94*x^4 - 55*x^5 - 17*x^6 + 13*x^7 + x^8) / ((1 - x)^2*(1 - x - x^2)^2). - Colin Barker, Feb 18 2019

Example

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

Crossrefs

Row 4 of A281205.

Sequence in context: A224739 A135176 A318625 * A100167 A100168 A137022

Adjacent sequences: A281205 A281206 A281207 * A281209 A281210 A281211

Keyword

nonn

Author

R. H. Hardin, Jan 17 2017

Status

approved