A204192 Number of n X 3 0..1 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order.

3, 18, 33, 86, 231, 639, 1724, 4697, 12763, 34668, 94209, 255980, 695507, 1889810, 5134844, 13952002, 37909418, 103004707, 279876923, 760461448, 2066270880, 5614322044, 15254830655, 41449324425, 112623111961, 306011389311

Offset

1,1

Comments

Column 3 of A204197.

Links

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

Formula

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

Empirical g.f.: x*(3 + 12*x - 12*x^2 - 31*x^3 - 7*x^4 + 48*x^5 + 25*x^6 - 34*x^7 - 14*x^8 + 5*x^9 + 4*x^10) / ((1 - x)*(1 + x)*(1 - 2*x - 2*x^2 - x^3 + 3*x^4 + x^5 - 2*x^6)). - Colin Barker, Jun 06 2018

Example

Some solutions for n=5:
..0..1..1....0..0..1....0..1..1....0..0..1....0..0..1....0..0..1....0..0..1
..0..1..1....0..1..0....1..0..0....0..1..1....1..0..0....1..1..0....0..1..0
..1..0..0....1..1..0....0..0..1....1..0..0....0..1..1....0..0..1....1..0..0
..0..0..1....1..0..1....1..1..0....1..0..1....1..0..0....0..1..0....0..1..1
..0..1..0....0..1..0....0..0..1....0..1..0....1..0..1....1..0..0....0..1..0

Crossrefs

Cf. A204197.

Sequence in context: A003337 A047714 A344188 * A108169 A063116 A125284

Adjacent sequences: A204189 A204190 A204191 * A204193 A204194 A204195

Keyword

nonn

Author

R. H. Hardin, Jan 12 2012

Status

approved