A209094 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

2, 11, 82, 612, 4568, 34096, 254496, 1899584, 14178688, 105831168, 789934592, 5896152064, 44009478144, 328491216896, 2451891822592, 18301169713152, 136601790414848, 1019609644466176, 7610469994070016, 56805321374695424

Offset

1,1

Comments

Column 2 of A209100.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 4*a(n-2) for n>3.

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: x*(2 - x)*(1 - 2*x) / (1 - 8*x + 4*x^2).

a(n) = ((4-2*sqrt(3))^n*(-1+sqrt(3)) + (1+sqrt(3))*(2*(2+sqrt(3)))^n) / (8*sqrt(3)) for n>1.

(End)

Example

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

Crossrefs

Cf. A209100.

Sequence in context: A309417 A215654 A330677 * A293574 A322644 A243408

Adjacent sequences: A209091 A209092 A209093 * A209095 A209096 A209097

Keyword

nonn

Author

R. H. Hardin, Mar 05 2012

Status

approved