A208065 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

10, 100, 240, 576, 1008, 1764, 2688, 4096, 5760, 8100, 10800, 14400, 18480, 23716, 29568, 36864, 44928, 54756, 65520, 78400, 92400, 108900, 126720, 147456, 169728, 195364, 222768, 254016, 287280, 324900, 364800, 409600, 456960, 509796, 565488

Offset

1,1

Comments

Column 4 of A208069.

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) for n>9.

Conjectures from Colin Barker, Jun 27 2018: (Start)

G.f.: 2*x*(5 + 40*x + 10*x^2 - 22*x^3 - 12*x^4 - 12*x^5 + 10*x^6 + 10*x^7 - 5*x^8) / ((1 - x)^5*(1 + x)^3).

a(n) = n^2*(n + 8)^2/4 for n>1 and even.

a(n) = (n - 1)*(n + 1)*(n + 7)*(n + 9)/4 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A208069.

Sequence in context: A119052 A029774 A208375 * A207930 A207847 A095920

Adjacent sequences: A208062 A208063 A208064 * A208066 A208067 A208068

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved