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

Author

R. H. Hardin, Dec 14 2011

Keywords

• nonn

Comments

Column 5 of A202202.

Examples

			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
		

Links

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

Crossrefs

Cf. A202202.

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)