A206336 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

192, 96, 455, 296, 1376, 880, 4111, 2622, 12319, 7854, 36945, 23550, 110823, 70638, 332457, 211902, 997359, 635694, 2992065, 1907070, 8976183, 5721198, 26928537, 17163582, 80785599, 51490734, 242356785, 154472190, 727070343, 463416558

Offset

1,1

Comments

Column 1 of A206343.

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>10.

Conjectures from Colin Barker, Jun 15 2018: (Start)

G.f.: x*(192 - 96*x - 217*x^2 + 129*x^3 + 3*x^4 - 19*x^5 - 9*x^6 - x^7 + 4*x^8 + 2*x^9) / ((1 - x)*(1 - 3*x^2)).

a(n) = 872 * 3^((n-9)/2+3/2) + 6 for n>7 and even.

a(n) = 12313 * 3^((n-9)/2) + 6 for n>7 and odd.

(End)

Example

Some solutions for n=4:
..1..1....2..1....1..3....0..3....3..0....3..0....0..1....0..1....1..0....1..1
..3..0....3..0....2..0....3..0....0..3....0..3....2..0....1..0....0..1....1..0
..0..3....0..3....0..2....0..3....2..0....3..0....0..2....0..1....2..0....0..1
..1..0....3..0....1..0....2..0....0..2....0..3....2..0....1..0....0..2....3..0
..0..1....0..3....0..1....0..2....1..0....1..1....0..2....0..1....3..1....0..3

Crossrefs

Cf. A206343.

Sequence in context: A187527 A187698 A206343 * A206335 A289219 A190892

Adjacent sequences: A206333 A206334 A206335 * A206337 A206338 A206339

Keyword

nonn

Author

R. H. Hardin, Feb 06 2012

Status

approved