A202197 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.

450, 1400, 3500, 7560, 14700, 26400, 44550, 71500, 110110, 163800, 236600, 333200, 459000, 620160, 823650, 1077300, 1389850, 1771000, 2231460, 2783000, 3438500, 4212000, 5118750, 6175260, 7399350, 8810200, 10428400, 12276000, 14376560

Offset

1,1

Comments

Column 3 of A202202.

Links

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

Formula

Empirical: a(n) = 5*(n+5)*(n+4)*(n+3)*(n+2)^2/12.

Conjectures from Colin Barker, May 27 2018: (Start)

G.f.: 10*x*(45 - 130*x + 185*x^2 - 144*x^3 + 59*x^4 - 10*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A202202.

Sequence in context: A351947 A079659 A304511 * A253750 A253743 A253369

Adjacent sequences: A202194 A202195 A202196 * A202198 A202199 A202200

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved