A242543 Number of length n+3 0..2 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..2 introduced in 0..2 order

12, 32, 88, 242, 660, 1800, 4920, 13448, 36736, 100352, 274176, 749088, 2046528, 5591168, 15275392, 41733248, 114017280, 311500800, 851036160, 2325074432, 6352221184, 17354590208, 47413622784, 129536428032, 353900101632

Offset

1,1

Comments

Column 2 of A242549

Links

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

Formula

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

Empirical: G.f.: -2*x*(6+4*x+12*x^2+9*x^3) / ( (2*x^2+2*x-1)*(2*x^2+1) ). - R. J. Mathar, May 18 2014

Example

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

Crossrefs

Sequence in context: A188183 A183682 A243027 * A194644 A068381 A143238

Adjacent sequences: A242540 A242541 A242542 * A242544 A242545 A242546

Keyword

nonn

Author

R. H. Hardin, May 17 2014

Status

approved