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

1,1

Comments

Column 2 of A269097.

Links

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

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)

Example

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

Crossrefs

Cf. A269097.

Sequence in context: A359653 A202682 A089639 * A204973 A204700 A267953

Adjacent sequences: A269088 A269089 A269090 * A269092 A269093 A269094

Keyword

nonn

Author

R. H. Hardin, Feb 19 2016

Status

approved