A202196 Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.

240, 640, 1400, 2688, 4704, 7680, 11880, 17600, 25168, 34944, 47320, 62720, 81600, 104448, 131784, 164160, 202160, 246400, 297528, 356224, 423200, 499200, 585000, 681408, 789264, 909440, 1042840, 1190400, 1353088, 1531904, 1727880, 1942080

Offset

1,1

Comments

Column 2 of A202202.

Links

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

Formula

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

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

G.f.: 8*x*(30 - 70*x + 75*x^2 - 39*x^3 + 8*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=6:
..0..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..1..1....1..1..1..1....1..1..1..1
..1..1..1..1....1..1..0..0....1..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..0..0....0..1..1..0....0..1..1..1
..1..1..0..0....1..1..0..0....0..0..0..0....0..1..1..0....0..1..1..0
..1..1..0..0....1..1..0..0....0..0..0..0....0..1..0..0....0..1..1..0

Crossrefs

Cf. A202202.

Sequence in context: A119659 A263161 A268772 * A060663 A092000 A124352

Adjacent sequences: A202193 A202194 A202195 * A202197 A202198 A202199

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved