A269091 Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

4, 96, 1152, 11424, 103488, 889056, 7375872, 59698464, 474360768, 3715826016, 28777886592, 220814937504, 1681292682048, 12718165610976, 95670977133312, 716203564928544, 5338972029467328, 39651633731043936, 293513242790716032

Offset: 1

Author

R. H. Hardin, Feb 19 2016

Keywords

• nonn

Comments

Column 2 of A269097.

Examples

			Some solutions for n=4:
..2..0. .2..2. .3..3. .3..3. .1..3. .3..3. .2..2. .3..2. .3..3. .1..3
..1..1. .2..2. .2..3. .2..2. .3..1. .0..1. .3..2. .2..3. .3..3. .0..1
..1..1. .1..0. .3..1. .1..3. .2..2. .1..0. .1..0. .0..1. .1..0. .0..2
..3..3. .3..2. .2..2. .3..3. .3..3. .0..1. .1..2. .0..2. .3..2. .2..2
		

Links

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

Crossrefs

Cf. A269097.

Formula

Empirical: a(n) = 14*a(n-1) -49*a(n-2) for n>3.

Conjectures from Colin Barker, Mar 21 2018: (Start)

G.f.: 4*x*(1 + 10*x + x^2) / (1 - 7*x)^2.

a(n) = 96*7^(n-3)*(5*n-3) for n>1.

(End)