A207020 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

9, 81, 252, 558, 1035, 1719, 2646, 3852, 5373, 7245, 9504, 12186, 15327, 18963, 23130, 27864, 33201, 39177, 45828, 53190, 61299, 70191, 79902, 90468, 101925, 114309, 127656, 142002, 157383, 173835, 191394, 210096, 229977, 251073, 273420, 297054

Offset: 1

Author

R. H. Hardin, Feb 14 2012

Keywords

• nonn

Comments

Column 4 of A207024.

Examples

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

Links

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

Crossrefs

Cf. A207024.

Formula

Empirical: a(n) = 6*n^3 + (27/2)*n^2 - (21/2)*n.

Conjectures from Colin Barker, Jun 17 2018: (Start)

G.f.: 9*x*(1 + 5*x - 2*x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)