A188556 Number of 5 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.

6, 11, 20, 36, 64, 112, 192, 321, 522, 825, 1268, 1898, 2772, 3958, 5536, 7599, 10254, 13623, 17844, 23072, 29480, 37260, 46624, 57805, 71058, 86661, 104916, 126150, 150716, 178994, 211392, 248347, 290326, 337827, 391380, 451548, 518928, 594152

Offset

1,1

Comments

Row 5 of A188553.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 - (1/24)*n^4 + (3/8)*n^3 + (1/24)*n^2 + (157/60)*n + 3.

Conjectures from Colin Barker, Apr 27 2018: (Start)

G.f.: x*(6 - 25*x + 44*x^2 - 39*x^3 + 18*x^4 - 3*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for 5 X 3:
..1..1..0....1..1..1....1..1..1....0..0..0....1..1..1....1..1..1....1..1..1
..0..0..0....1..1..1....0..0..0....0..0..0....1..1..0....1..1..1....1..1..1
..0..0..0....1..1..1....0..0..0....0..0..0....1..0..0....1..1..1....1..1..1
..0..0..0....1..1..0....0..0..0....0..0..0....0..0..0....1..1..0....1..1..1
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

Crossrefs

Cf. A188553.

Sequence in context: A160842 A365351 A007745 * A021011 A000382 A208670

Adjacent sequences: A188553 A188554 A188555 * A188557 A188558 A188559

Keyword

nonn

Author

R. H. Hardin, Apr 04 2011

Status

approved