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

1,1

Comments

Row 8 of A188553.

Links

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

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)

Example

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

Crossrefs

Cf. A188553.

Sequence in context: A228260 A147459 A352789 * A014004 A090994 A164887

Adjacent sequences: A188556 A188557 A188558 * A188560 A188561 A188562

Keyword

nonn

Author

R. H. Hardin, Apr 04 2011

Status

approved