A208556 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

9, 81, 225, 1089, 3969, 16641, 65025, 263169, 1046529, 4198401, 16769025, 67125249, 268402689, 1073807361, 4294836225, 17180131329, 68718952449, 274878955521, 1099509530625, 4398050705409, 17592177655809, 70368760954881

Offset: 1

Author

R. H. Hardin, Feb 28 2012

Keywords

• nonn

Comments

Row 4 of A208555.

It seems that all terms are squares. - Colin Barker, Mar 07 2018

Examples

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

Links

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

Crossrefs

Cf. A208555.

Formula

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

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: 9*x*(1 + 6*x - 8*x^2) / ((1 - x)*(1 + 2*x)*(1 - 4*x)).

a(n) = (2^(n+1) + 1)^2 for n even.

a(n) = (2^(n+1) - 1)^2 for n odd.

(End)