A240778 Number of n X 3 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.

1, 4, 20, 97, 459, 2187, 10442, 49861, 238068, 1136678, 5427201, 25912833, 123723975, 590735140, 2820536641, 13466994652, 64299801122, 307007207679, 1465843189533, 6998846289463, 33416841401200, 159552766705917

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - a(n-2) - a(n-3) + 4*a(n-4) - 4*a(n-5) - 3*a(n-6) + a(n-7).

Empirical g.f.: x*(1 + x)^2*(1 - 3*x + 6*x^2 - 7*x^3 + 2*x^4) / ((1 - x)*(1 - 4*x - 3*x^2 - 2*x^3 - 6*x^4 - 2*x^5 + x^6)). - Colin Barker, Oct 29 2018

Example

Some solutions for n=4:
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..0..1..1....1..0..1....0..1..0....0..1..0....0..1..0....1..0..1....1..1..0
..0..1..1....0..1..1....1..0..1....1..1..0....0..0..1....1..1..0....1..0..0
..0..1..0....0..1..0....0..1..0....1..1..0....1..0..1....0..1..0....1..0..0

Crossrefs

Column 3 of A240783.

Sequence in context: A057087 A151254 A232493 * A293710 A098225 A073532

Adjacent sequences: A240775 A240776 A240777 * A240779 A240780 A240781

Keyword

nonn

Author

R. H. Hardin, Apr 12 2014

Status

approved