A188828 Number of 6 X n binary arrays without the pattern 0 1 diagonally or antidiagonally.

64, 49, 169, 576, 2025, 7056, 24964, 87616, 310249, 1092025, 3865156, 13623481, 48191364, 169989444, 601034256, 2121063025, 7496962225, 26464782400, 93519144481, 330192741376, 1166628971236, 4119600902400, 14553774833481

Offset

1,1

Comments

Row 6 of A188824.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +9*a(n-2) -45*a(n-3) +108*a(n-5) -42*a(n-6) -57*a(n-7) +18*a(n-8) +7*a(n-9) -a(n-10) for n>11.

Empirical g.f.: x*(64 - 207*x - 603*x^2 + 2339*x^3 + 405*x^4 - 5535*x^5 + 1831*x^6 + 2835*x^7 - 840*x^8 - 340*x^9 + 48*x^10) / ((1 - x)*(1 - 6*x + 9*x^2 - x^3)*(1 + 3*x - x^3)*(1 - 3*x^2 - x^3)). - Colin Barker, Apr 30 2018

Example

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

Crossrefs

Cf. A188824.

Sequence in context: A169639 A252486 A382946 * A331224 A123994 A248770

Adjacent sequences: A188825 A188826 A188827 * A188829 A188830 A188831

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved