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

Author

R. H. Hardin, Feb 14 2012

Keywords

• nonn

Comments

Column 3 of A206987.

Examples

			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
		

Links

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

Crossrefs

Cf. A206987.

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