A202428 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 001 in rows, columns and nw-to-se diagonals.

108, 390, 1344, 4680, 16254, 56508, 196350, 682452, 2371680, 8242608, 28645968, 99555660, 345992850, 1202454762, 4178979168, 14523514614, 50474639160, 175418231664, 609643897626, 2118740336046, 7363414320192, 25590616062900

Offset

1,1

Comments

Column 1 of A202435.

Links

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

Formula

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

Empirical g.f.: 6*x*(18 + 47*x + 33*x^2 - 7*x^3 - 11*x^4 + 6*x^5) / (1 - x - 7*x^2 - 6*x^3 + x^4 + 2*x^5 - x^6). - Colin Barker, May 28 2018

Example

Some solutions for n=5:
..1..1..1....1..0..0....1..1..1....0..1..1....1..1..1....0..1..0....1..1..1
..1..1..1....0..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..0..1
..1..0..1....1..1..1....0..1..1....1..0..0....1..1..1....1..1..1....1..1..0
..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....0..1..1
..1..1..1....0..1..1....1..1..0....0..1..1....1..1..1....1..1..1....1..1..0
..1..0..0....1..1..1....1..0..1....1..1..0....1..0..1....0..1..1....0..1..1
..1..1..0....0..1..0....0..1..0....1..1..0....1..1..1....1..1..0....0..1..0

Crossrefs

Cf. A202435.

Sequence in context: A192793 A182171 A202435 * A224526 A251270 A255083

Adjacent sequences: A202425 A202426 A202427 * A202429 A202430 A202431

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved