A202310 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 100 in rows and columns.

108, 333, 1144, 4048, 14743, 54250, 201098, 747683, 2785178, 10383774, 38732585, 144511028, 539243500, 2012324661, 7509786472, 28026278000, 104594259855, 390348614698, 1456795959866, 5436826706395, 20290493971290, 75725115284622

Offset

1,1

Comments

Column 1 of A202317.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -5*a(n-2) -22*a(n-3) +32*a(n-4) +16*a(n-5) -35*a(n-6) +2*a(n-7) +9*a(n-8) -2*a(n-9).

Empirical g.f.: x*(108 - 315*x - 314*x^2 + 1225*x^3 + 45*x^4 - 1184*x^5 + 213*x^6 + 290*x^7 - 72*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 4*x + x^2)*(1 + x - x^2)*(1 - x - x^2)). - Colin Barker, Feb 14 2018

Example

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

Crossrefs

Sequence in context: A202093 A202485 A202317 * A192793 A182171 A202435

Adjacent sequences: A202307 A202308 A202309 * A202311 A202312 A202313

Keyword

nonn

Author

R. H. Hardin, Dec 16 2011

Status

approved