A202440 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

80, 138, 224, 338, 484, 666, 888, 1154, 1468, 1834, 2256, 2738, 3284, 3898, 4584, 5346, 6188, 7114, 8128, 9234, 10436, 11738, 13144, 14658, 16284, 18026, 19888, 21874, 23988, 26234, 28616, 31138, 33804, 36618, 39584, 42706, 45988, 49434, 53048, 56834

Offset

1,1

Comments

Column 1 of A202447.

Links

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

Formula

Empirical: a(n) = (2/3)*n^3 + 8*n^2 + (100/3)*n + 34 for n>1.

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

G.f.: 2*x*(40 - 91*x + 76*x^2 - 25*x^3 + 2*x^4) / (1 - x)^4.

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

(End)

Example

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

Crossrefs

Cf. A202447.

Sequence in context: A224547 A204648 A202447 * A248432 A107931 A234134

Adjacent sequences: A202437 A202438 A202439 * A202441 A202442 A202443

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved