A206982 Number of n X 3 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal.

6, 36, 58, 158, 420, 1066, 2754, 7140, 18430, 47602, 123028, 317870, 821262, 2121988, 5482746, 14166078, 36601876, 94570810, 244348930, 631340852, 1631238222, 4214740594, 10889910564, 28136999454, 72699470734, 187838545012

Offset

1,1

Comments

Column 3 of A206987.

Links

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

Formula

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

Empirical g.f.: 2*x*(1 - x)*(3 + 15*x + 5*x^2 + 2*x^3 - 8*x^4 - 8*x^5) / (1 - 2*x - x^2 - 2*x^3 + x^4 + 2*x^5). - Colin Barker, Jun 17 2018

Example

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

Crossrefs

Cf. A206987.

Sequence in context: A132633 A047792 A178909 * A121026 A207694 A208496

Adjacent sequences: A206979 A206980 A206981 * A206983 A206984 A206985

Keyword

nonn

Author

R. H. Hardin, Feb 14 2012

Status

approved