A208705 Number of n X 4 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

8, 100, 1268, 16084, 204020, 2587924, 32826932, 416398420, 5281871732, 66998738836, 849856117940, 10780134577876, 136742325040628, 1734529687216660, 22001916633654068, 279086797488636244

Offset

1,1

Comments

Column 4 of A208709.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 4*a(n-2).

Conjectures from Colin Barker, Jul 06 2018: (Start)

G.f.: 4*x*(2 - x) / (1 - 13*x + 4*x^2).

a(n) = (2^(-1-n)*((13-3*sqrt(17))^n*(-1+sqrt(17)) + (1+sqrt(17))*(13+3*sqrt(17))^n)) / sqrt(17).

(End)

Example

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

Crossrefs

Cf. A208709

Sequence in context: A179485 A144072 A261800 * A246237 A234513 A251686

Adjacent sequences: A208702 A208703 A208704 * A208706 A208707 A208708

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved