A206931 Number of n X 3 0..1 arrays avoiding 0 0 0 horizontally and 0 1 1 vertically.

7, 49, 211, 811, 2791, 9055, 28081, 84403, 247705, 713857, 2027929, 5695201, 15845455, 43747201, 120004363, 327401947, 889103743, 2404885423, 6482464537, 17421401395, 46696588561, 124877198881, 333267920209, 887801858209

Offset

1,1

Comments

Column 3 of A206936.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) - 6*a(n-3) + 18*a(n-4) - 9*a(n-6) + a(n-8).

Empirical g.f.: x*(7 + 7*x - 20*x^2 + 28*x^3 - 8*x^4 - 8*x^5 + x^6 + x^7) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 2*x - x^2)). - Colin Barker, Jun 17 2018

Example

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

Crossrefs

Cf. A206936.

Sequence in context: A373684 A294292 A015953 * A188608 A188601 A206866

Adjacent sequences: A206928 A206929 A206930 * A206932 A206933 A206934

Keyword

nonn

Author

R. H. Hardin, Feb 13 2012

Status

approved