A206989 Number of n X 3 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

7, 49, 174, 840, 3858, 17460, 80070, 365784, 1670838, 7636416, 34893438, 159444240, 728589330, 3329288484, 15213221238, 69517022592, 317658800982, 1451545657152, 6632855083422, 30308909178984, 138496917825186, 632863297956804

Offset

1,1

Comments

Column 3 of A206994.

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) - 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7) for n>9.

Empirical g.f.: x*(1 - x)*(7 + 35*x + 27*x^2 + 23*x^3 - 13*x^4 - 3*x^5 - x^6 + x^7) / (1 - 3*x - 5*x^2 - 11*x^3 + 5*x^4 - x^5 + 3*x^6 - x^7). - Colin Barker, Jun 17 2018

Example

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

Crossrefs

Cf. A206994.

Sequence in context: A003530 A262269 A163827 * A221962 A294292 A015953

Adjacent sequences: A206986 A206987 A206988 * A206990 A206991 A206992

Keyword

nonn

Author

R. H. Hardin, Feb 14 2012

Status

approved