A202445 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

666, 1162, 2544, 4822, 8996, 15314, 25576, 40126, 61820, 91098, 132128, 185446, 256788, 346786, 463000, 606158, 785900, 1003050, 1269584, 1586422, 1968132, 2415730, 2946632, 3561950, 4282204, 5108602, 6065024, 7152774, 8399348, 9806146

Offset

1,1

Comments

Column 6 of A202447.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9) for n>10.

Empirical g.f.: 2*x*(333 - 418*x - 471*x^2 + 1259*x^3 - 85*x^4 - 1145*x^5 + 651*x^6 + 233*x^7 - 300*x^8 + 71*x^9) / ((1 - x)^6*(1 + x)^3). - Colin Barker, May 31 2018

Example

Some solutions for n=4:
..0..0..0..0..0..0..0..0....0..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..1..0..1..0..1..0..1....0..1..0..0..0..0..0..0....0..1..0..0..0..0..0..0
..0..0..0..0..0..0..0..0....0..1..0..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..1..0..1..0..1..0..1....0..1..0..1..0..0..0..0....0..1..1..1..1..1..1..1
..0..1..0..0..0..0..0..0....0..1..0..1..0..1..1..1....0..1..1..1..1..1..1..1
..0..1..0..1..0..1..0..1....0..1..0..1..0..1..0..0....0..1..1..1..1..1..1..1

Crossrefs

Cf. A202447.

Sequence in context: A069426 A093733 A133562 * A062045 A043515 A051003

Adjacent sequences: A202442 A202443 A202444 * A202446 A202447 A202448

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved