A202201 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.

2430, 11880, 44550, 138996, 378378, 926640, 2084940, 4375800, 8664084, 16325712, 29476980, 51279480, 86337900, 141210432, 225054126, 350430300, 534298050, 799227000, 1174863690, 1699689420, 2423110950, 3407929200, 4733235000

Offset

1,1

Comments

Column 7 of A202202.

Links

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

Formula

Empirical: a(n) = (n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/2240.

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

G.f.: 18*x*(135 - 690*x + 1950*x^2 - 3528*x^3 + 4326*x^4 - 3660*x^5 + 2115*x^6 - 800*x^7 + 179*x^8 - 18*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Cf. A202202.

Sequence in context: A186874 A345174 A345175 * A147984 A229871 A192767

Adjacent sequences: A202198 A202199 A202200 * A202202 A202203 A202204

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved