A269146 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

4, 80, 768, 6224, 46464, 330192, 2270592, 15251152, 100647168, 655139152, 4217820672, 26911075152, 170416738944, 1072338720464, 6710943646848, 41800542176720, 259288295447040, 1602497927690832, 9871915467776256

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.

Empirical g.f.: 4*x*(1 - x)*(1 + 9*x - x^2 - x^3) / (1 - 6*x + x^2)^2. - Colin Barker, Jan 19 2019

Example

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

Crossrefs

Column 2 of A269152.

Sequence in context: A093854 A345459 A366955 * A192834 A054322 A114488

Adjacent sequences: A269143 A269144 A269145 * A269147 A269148 A269149

Keyword

nonn

Author

R. H. Hardin, Feb 20 2016

Status

approved