A188823 Number of n X 8 binary arrays without the pattern 0 1 diagonally or antidiagonally.

256, 3025, 11664, 28561, 53824, 87616, 129600, 179776, 238144, 304704, 379456, 462400, 553536, 652864, 760384, 876096, 1000000, 1132096, 1272384, 1420864, 1577536, 1742400, 1915456, 2096704, 2286144, 2483776, 2689600, 2903616, 3125824

Offset

1,1

Comments

Column 8 of A188824.

Links

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

Formula

Empirical: a(n) = 4096*n^2 - 11264*n + 7744 for n>4.

Empirical g.f.: x*(256 + 2257*x + 3357*x^2 + 2388*x^3 + 108*x^4 + 163*x^5 - 337*x^6) / (1 - x)^3. - Colin Barker, Apr 30 2018

Example

Some solutions for 3 X 8:
..1..1..1..0..1..0..1..0....1..1..0..1..1..1..1..1....0..1..1..1..1..1..1..1
..0..1..0..1..0..1..0..0....1..0..1..0..1..1..0..1....0..0..1..0..1..1..1..0
..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1

Crossrefs

Cf. A188824.

Sequence in context: A235502 A236202 A236199 * A205935 A205928 A235665

Adjacent sequences: A188820 A188821 A188822 * A188824 A188825 A188826

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved