A240513 Number of n X 2 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order.

2, 3, 6, 10, 21, 42, 86, 179, 370, 770, 1601, 3330, 6930, 14419, 30006, 62442, 129941, 270410, 562726, 1171043, 2436962, 5071362, 10553601, 21962242, 45703842, 95110563, 197926886, 411889610, 857150101, 1783745642, 3712008566, 7724760339

Offset

1,1

Comments

Column 2 of A240519.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) + a(n-5).

Empirical g.f.: x*(2 - x)*(1 - x^2 - 2*x^3) / ((1 - x)*(1 - x - 2*x^2 - x^3 + x^4)). - Colin Barker, Feb 24 2018

Empirical: a(n) = 1+A105309(n). - R. J. Mathar, Nov 09 2018

Example

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

Crossrefs

Cf. A240519.

Sequence in context: A211180 A265582 A242563 * A036650 A049889 A014270

Adjacent sequences: A240510 A240511 A240512 * A240514 A240515 A240516

Keyword

nonn

Author

R. H. Hardin, Apr 06 2014

Status

approved