A188559 Number of 8 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.

9, 17, 32, 60, 112, 208, 384, 704, 1280, 2304, 4097, 7181, 12381, 20965, 34831, 56751, 90683, 142163, 218790, 330818, 491870, 719790, 1037650, 1474930, 2068890, 2866154, 3924527, 5315067, 7124435, 9457547, 12440553, 16224169, 20987389

Offset: 1

Author

R. H. Hardin, Apr 04 2011

Keywords

• nonn

Comments

Row 8 of A188553.

Examples

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

Links

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

Crossrefs

Cf. A188553.

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (19/2880)*n^6 - (7/180)*n^5 + (1247/5760)*n^4 - (85/288)*n^3 + (17911/10080)*n^2 + (1961/840)*n + 5.

Conjectures from Colin Barker, Apr 28 2018: (Start)

G.f.: x*(9 - 64*x + 203*x^2 - 372*x^3 + 430*x^4 - 320*x^5 + 150*x^6 - 40*x^7 + 5*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)