A202640 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 111 in rows, columns and nw-to-se diagonals.

66, 172, 462, 1278, 3448, 9394, 25526, 69336, 188418, 511960, 1391014, 3779620, 10269688, 27904004, 75818836, 206009414, 559753846, 1520922896, 4132541760, 11228644088, 30509661310, 82898648850, 225246223922, 612022778622

Offset

1,1

Comments

Column 1 of A202647.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -5*a(n-4) -2*a(n-5) +5*a(n-6) +a(n-7) -2*a(n-8) for n>9.

Empirical g.f.: 2*x*(33 + 20*x - 40*x^2 - 48*x^3 + 4*x^4 + 59*x^5 - 2*x^6 - 31*x^7 + 4*x^8) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - x^3 + 3*x^4 + x^5 - 2*x^6)). - Colin Barker, Jun 01 2018

Example

Some solutions for n=3:
..1..0..1....0..1..0....1..0..1....1..0..0....1..0..1....0..1..0....1..1..0
..0..1..1....1..0..0....0..1..0....1..0..0....0..1..1....1..0..1....0..0..1
..0..1..0....0..1..1....0..1..0....0..1..1....1..1..0....0..0..1....0..1..0
..1..0..0....1..0..0....1..0..1....0..1..0....0..0..1....0..1..0....1..0..0
..1..0..1....1..0..1....0..1..1....1..0..0....0..0..1....1..0..1....0..0..1

Crossrefs

Cf. A202647.

Sequence in context: A249284 A255102 A202647 * A074873 A205817 A046393

Adjacent sequences: A202637 A202638 A202639 * A202641 A202642 A202643

Keyword

nonn

Author

R. H. Hardin, Dec 22 2011

Status

approved