A206121 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors.

50, 170, 558, 1906, 6386, 21940, 74714, 258496, 891586, 3106540, 10821426, 37946232, 133190826, 469570860, 1657721338, 5869905680, 20812541098, 73947974244, 263041695362, 937043382992, 3341162160402, 11925776401308

Offset

1,1

Comments

Column 1 of A206128.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 13*a(n-2) - 9*a(n-3) - 50*a(n-4) - 43*a(n-5) + 4*a(n-6) - 4*a(n-8) for n>9.

Empirical g.f.: 2*x*(25 + 35*x - 216*x^2 - 485*x^3 - 325*x^4 + 31*x^5 - 10*x^6 - 32*x^7 - x^8) / ((1 - 8*x^2 - 4*x^3)*(1 - 2*x - 5*x^2 - 3*x^3 + 2*x^4 - x^5)). - Colin Barker, Jun 13 2018

Example

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

Crossrefs

Cf. A206128.

Sequence in context: A048511 A206128 A333101 * A349808 A244696 A244697

Adjacent sequences: A206118 A206119 A206120 * A206122 A206123 A206124

Keyword

nonn

Author

R. H. Hardin, Feb 04 2012

Status

approved