A208402 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

2, 15, 187, 2795, 43947, 700075, 11188907, 178973355, 2863377067, 45813246635, 733008800427, 11728128223915, 187650001250987, 3002399818689195, 48038396293720747, 768614337478306475, 12297829386768001707

Offset

1,1

Comments

Column 2 of A208408.

Links

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

Formula

Empirical: a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).

Conjectures from Colin Barker, Jul 02 2018: (Start)

G.f.: x*(2 - 27*x + 40*x^2) / ((1 - x)*(1 - 4*x)*(1 - 16*x)).

a(n) = (8 + 3*2^(1+2*n) + 16^n) / 24.

(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..0
..0..0....0..1....1..0....0..0....0..0....0..1....0..1....0..0....1..1....1..0
..1..1....0..0....0..2....0..1....1..2....1..0....0..0....1..0....0..0....2..0
..2..0....1..0....2..0....1..0....3..2....1..1....0..2....2..2....0..1....1..2

Crossrefs

Cf. A208408.

Sequence in context: A053492 A319834 A268420 * A098343 A052819 A349292

Adjacent sequences: A208399 A208400 A208401 * A208403 A208404 A208405

Keyword

nonn

Author

R. H. Hardin, Feb 26 2012

Status

approved