A202199 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.

1176, 4704, 14700, 38808, 90552, 192192, 378378, 700700, 1233232, 2079168, 3378648, 5317872, 8139600, 12155136, 17757894, 25438644, 35802536, 49588000, 67687620, 91171080, 121310280, 159606720, 207821250, 268006284, 342540576

Offset

1,1

Comments

Column 5 of A202202.

Links

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

Formula

Empirical: a(n) = 7*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/360.

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

G.f.: 14*x*(84 - 336*x + 714*x^2 - 924*x^3 + 756*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=2:
..1..1..1..1..1..1..0....1..1..1..0..0..0..0....0..1..1..1..1..1..1
..1..1..1..1..1..0..0....1..1..1..1..1..1..1....1..1..1..1..1..0..0
..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..1..1..1..0..0..0
..1..0..0..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0

Crossrefs

Cf. A202202.

Sequence in context: A204756 A027485 A204755 * A233870 A237774 A223340

Adjacent sequences: A202196 A202197 A202198 * A202200 A202201 A202202

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved