A188557 Number of 6 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.

7, 13, 24, 44, 80, 144, 256, 448, 769, 1291, 2116, 3384, 5282, 8054, 12012, 17548, 25147, 35401, 49024, 66868, 89940, 119420, 156680, 203304, 261109, 332167, 418828, 523744, 649894, 800610, 979604, 1190996, 1439343, 1729669, 2067496, 2458876

Offset

1,1

Comments

Row 6 of A188553.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 - (1/80)*n^5 + (17/144)*n^4 - (3/16)*n^3 + (497/360)*n^2 + (17/10)*n + 4.

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

G.f.: x*(7 - 36*x + 80*x^2 - 96*x^3 + 66*x^4 - 24*x^5 + 4*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for 6 X 3:
..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..0....1..1..1....1..1..1....1..1..1....0..0..0
..1..1..1....1..1..1....0..0..0....1..1..1....1..1..1....1..1..1....0..0..0
..1..1..0....1..1..0....0..0..0....1..1..1....1..1..1....1..1..1....0..0..0
..0..0..0....1..0..0....0..0..0....1..1..0....1..1..1....1..1..0....0..0..0
..0..0..0....0..0..0....0..0..0....1..0..0....1..1..1....0..0..0....0..0..0

Crossrefs

Cf. A188553.

Sequence in context: A228727 A286916 A032690 * A356966 A090992 A259215

Adjacent sequences: A188554 A188555 A188556 * A188558 A188559 A188560

Keyword

nonn

Author

R. H. Hardin, Apr 04 2011

Status

approved