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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 12 2012
STATUS
approved