A202049 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns.

966, 3304, 9170, 22092, 47950, 95984, 180054, 320180, 544390, 890904, 1410682, 2170364, 3255630, 4775008, 6864158, 9690660, 13459334, 18418120, 24864546, 33152812, 43701518, 57002064, 73627750, 94243604, 119616966, 150628856

Offset

1,1

Comments

Column 5 of A202052.

Links

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

Formula

Empirical: a(n) = (1/180)*n^7 + (7/36)*n^6 + (511/180)*n^5 + (805/36)*n^4 + (4606/45)*n^3 + (2443/9)*n^2 + (1854/5)*n + 196.

Conjectures from Colin Barker, May 26 2018: (Start)

G.f.: 14*x*(69 - 316*x + 699*x^2 - 918*x^3 + 755*x^4 - 384*x^5 + 111*x^6 - 14*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

Some solutions for n=3:
..0..1..0..1..0..1..0....0..1..1..1..1..1..1....0..1..0..1..0..0..0
..1..0..1..0..1..0..1....1..0..1..0..1..0..0....1..0..1..1..1..1..1
..0..1..0..1..0..1..0....1..1..1..1..1..1..1....0..1..0..1..0..0..0
..0..0..0..0..0..0..0....1..0..1..0..1..0..1....0..1..0..1..0..1..0
..0..1..0..0..0..0..0....1..0..1..0..1..1..1....0..1..0..1..0..0..0

Crossrefs

Cf. A202052.

Sequence in context: A014363 A260291 A251232 * A246477 A064258 A142378

Adjacent sequences: A202046 A202047 A202048 * A202050 A202051 A202052

Keyword

nonn

Author

R. H. Hardin, Dec 10 2011

Status

approved