A189105 Number of n X 3 binary arrays without the pattern 1 1 0 diagonally or antidiagonally.

8, 64, 400, 2500, 15200, 92416, 560576, 3400336, 20623296, 125081856, 758633088, 4601180224, 27906627456, 169256542464, 1026558406656, 6226182733824, 37762441850880, 229033113145600, 1389109506607360, 8425092751196416

Offset

1,1

Comments

Column 3 of A189111.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -40*a(n-3) +22*a(n-4) +86*a(n-5) -80*a(n-6) +24*a(n-8) -8*a(n-9).

Empirical g.f.: 4*x*(2 + 2*x - 12*x^2 + 5*x^3 + 21*x^4 - 20*x^5 + 6*x^7 - 2*x^8) / ((1 - 7*x + 6*x^2 - 2*x^3)*(1 - 6*x^2 + 14*x^4 - 4*x^6)). - Colin Barker, May 01 2018

Example

Some solutions for 4 X 3:
..1..1..0....1..1..1....0..1..0....0..1..1....0..0..0....0..1..0....0..1..1
..1..0..1....0..0..0....1..0..0....1..1..0....1..0..0....0..1..0....1..0..1
..0..0..1....0..0..1....0..0..1....1..0..1....1..0..0....0..1..1....1..0..1
..1..0..1....1..1..1....0..0..0....0..1..1....1..0..0....0..1..0....0..1..1

Crossrefs

Cf. A189111.

Sequence in context: A297376 A293888 A218267 * A181214 A283859 A222446

Adjacent sequences: A189102 A189103 A189104 * A189106 A189107 A189108

Keyword

nonn

Author

R. H. Hardin, Apr 16 2011

Status

approved