A207363 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

6, 36, 90, 225, 420, 784, 1260, 2025, 2970, 4356, 6006, 8281, 10920, 14400, 18360, 23409, 29070, 36100, 43890, 53361, 63756, 76176, 89700, 105625, 122850, 142884, 164430, 189225, 215760, 246016, 278256, 314721, 353430, 396900, 442890, 494209

Offset

1,1

Comments

Column 3 of A207368.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

Conjectures from Colin Barker, Feb 21 2018: (Start)

G.f.: x*(6 + 24*x + 6*x^2 + 9*x^3 + 6*x^4 - 2*x^5 - 2*x^6 + x^7)/ ((1 - x)^5*(1 + x)^3).

a(n) = (n^4 + 6*n^3 + 13*n^2 + 12*n + 4) / 4 for n even.

a(n) = (n^4 + 6*n^3 + 11*n^2 + 6*n) / 4 for n odd.

(End)

Example

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

Crossrefs

Cf. A207368.

Sequence in context: A207656 A207341 A152746 * A207600 A207026 A207171

Adjacent sequences: A207360 A207361 A207362 * A207364 A207365 A207366

Keyword

nonn

Author

R. H. Hardin, Feb 17 2012

Status

approved