A203176 Number of n X 3 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.

2, 2, 7, 17, 41, 97, 235, 607, 1415, 3486, 8648, 20838, 51170, 124939, 305270, 746199, 1820662, 4454559, 10877169, 26569604, 64944236, 158629072, 387600053, 946993492, 2313654220, 5653010591, 13810992779, 33744134975, 82444452049

Offset

1,1

Comments

Column 3 of A203181.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) +10*a(n-3) +5*a(n-4) -a(n-5) -31*a(n-6) -7*a(n-7) +30*a(n-9) for n>10.

Empirical G.f.:

2*x -x^2*(2+7*x+13*x^2+7*x^3-17*x^4-50*x^5-13*x^6+18*x^7+54*x^8) / ( -1+2*x^2+10*x^3+5*x^4-x^5-31*x^6-7*x^7+30*x^9 ). - R. J. Mathar, Jul 02 2013

Example

Some solutions for n=5:
..0..1..2....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0
..1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
..2..1..0....0..1..2....0..1..0....2..1..0....0..1..0....0..1..2....2..1..2
..0..1..1....1..0..1....1..0..1....0..2..1....1..2..1....1..0..1....0..1..0
..1..0..2....0..1..0....0..1..0....1..0..2....2..0..1....0..1..2....1..0..1

Crossrefs

Sequence in context: A192921 A051769 A256400 * A203579 A338415 A243022

Adjacent sequences: A203173 A203174 A203175 * A203177 A203178 A203179

Keyword

nonn

Author

R. H. Hardin, Dec 30 2011

Status

approved