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

Author

R. H. Hardin, Apr 11 2011

Keywords

• nonn

Comments

Column 8 of A188824.

Examples

			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
		

Links

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

Crossrefs

Cf. A188824.

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