A202584 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 100 in rows, columns and nw-to-se diagonals.

96, 260, 804, 2554, 8372, 27649, 91973, 306486, 1023025, 3416176, 11412046, 38126620, 127389228, 425644289, 1422231173, 4752212465, 15879019404, 53058142574, 177288642743, 592392993030, 1979424904812, 6614060706429

Offset

1,1

Comments

Column 1 of A202591.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +5*a(n-2) -11*a(n-3) -10*a(n-4) +9*a(n-5) +12*a(n-6) -2*a(n-7) -6*a(n-8) +a(n-10).

Empirical g.f.: x*(96 - 28*x - 456*x^2 - 102*x^3 + 510*x^4 + 343*x^5 - 192*x^6 - 210*x^7 + 23*x^8 + 36*x^9) / ((1 - x)*(1 + x - x^2)*(1 - x - x^2)*(1 - 2*x - 4*x^2 - 2*x^3 + x^4 + x^5)). - Colin Barker, Feb 14 2018

Example

Some solutions for n=3:
..1..1..0....1..1..1....1..1..1....1..1..0....0..1..0....1..0..1....0..1..0
..1..1..1....1..1..1....0..1..1....1..1..1....0..1..0....0..1..0....1..1..1
..0..0..0....1..0..1....1..1..1....0..1..1....0..0..0....1..0..1....0..1..1
..1..1..1....1..1..1....0..1..1....1..1..1....0..1..0....1..1..0....1..1..1
..1..1..1....0..1..0....1..0..1....1..1..0....0..0..0....1..0..1....0..1..1

Crossrefs

Sequence in context: A202891 A232939 A202591 * A062027 A320883 A048189

Adjacent sequences: A202581 A202582 A202583 * A202585 A202586 A202587

Keyword

nonn

Author

R. H. Hardin, Dec 21 2011

Status

approved