A188821 Number of n X 6 binary arrays without the pattern 0 1 diagonally or antidiagonally.

64, 441, 1296, 2704, 4624, 7056, 10000, 13456, 17424, 21904, 26896, 32400, 38416, 44944, 51984, 59536, 67600, 76176, 85264, 94864, 104976, 115600, 126736, 138384, 150544, 163216, 176400, 190096, 204304, 219024, 234256, 250000, 266256, 283024

Offset

1,1

Comments

Column 6 of A188824.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 256*n^2 - 384*n + 144 for n>2.

Conjectures from Colin Barker, Apr 30 2018: (Start)

G.f.: x*(64 + 249*x + 165*x^2 + 75*x^3 - 41*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

(End)

Example

Some solutions for 3 X 6:
..0..1..1..1..1..1....1..1..1..1..1..1....1..0..1..1..1..1....0..1..0..1..1..1
..0..0..1..0..1..0....0..1..1..1..1..1....0..1..0..1..0..1....1..0..1..0..1..1
..0..0..0..1..0..0....0..0..1..1..1..1....1..0..1..0..1..0....0..1..0..0..0..0

Crossrefs

Cf. A188824.

Sequence in context: A188785 A317237 A282771 * A181210 A092211 A130812

Adjacent sequences: A188818 A188819 A188820 * A188822 A188823 A188824

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved