A207142 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

50, 30, 80, 62, 159, 122, 315, 242, 628, 482, 1254, 962, 2506, 1922, 5010, 3842, 10018, 7682, 20034, 15362, 40066, 30722, 80130, 61442, 160258, 122882, 320514, 245762, 641026, 491522, 1282050, 983042, 2564098, 1966082, 5128194, 3932162, 10256386

Offset

1,1

Comments

Column 1 of A207149.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n>8.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: x*(50 - 20*x - 50*x^2 + 22*x^3 - 3*x^4 - x^5 - x^6 + x^7) / ((1 - x)*(1 - 2*x^2)).

a(n) = 15 * 2^(n/2) + 2 for n>5 and even.

a(n) = 313 * 2^((n-7)/2) + 2 for n>5 and odd.

(End)

Example

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

Crossrefs

Cf. A207149.

Sequence in context: A033980 A342903 A207149 * A244277 A248688 A291495

Adjacent sequences: A207139 A207140 A207141 * A207143 A207144 A207145

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved