A283852 Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.

8, 61, 409, 2837, 19776, 137459, 955680, 6645662, 46211001, 321328965, 2234376733, 15536845232, 108036163039, 751234447860, 5223743482218, 36323541679065, 252577425569649, 1756308801126965, 12212574412144160, 84920700547463563

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 2*a(n-2) + 19*a(n-3) - 50*a(n-4) - 2*a(n-5) - 48*a(n-6) + 88*a(n-7) - 32*a(n-8).

Empirical g.f.: x*(8 + 5*x - 2*x^2 - 56*x^3 - 24*x^4 - 4*x^5 + 72*x^6 - 32*x^7) / (1 - 7*x + 2*x^2 - 19*x^3 + 50*x^4 + 2*x^5 + 48*x^6 - 88*x^7 + 32*x^8). - Colin Barker, Feb 22 2019

Example

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

Crossrefs

Column 3 of A283857.

Sequence in context: A007399 A071401 A247535 * A283410 A081907 A278596

Adjacent sequences: A283849 A283850 A283851 * A283853 A283854 A283855

Keyword

nonn

Author

R. H. Hardin, Mar 17 2017

Status

approved