A269271 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

24, 1368, 46872, 1365336, 36673560, 938176344, 23230366488, 561939624792, 13356872620056, 313173275509080, 7262896745936664, 166932248829835608, 3808216985895026712, 86327991673633618776, 1946351959512905208600

Offset

1,1

Links

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

Formula

Empirical: a(n) = 42*a(n-1) - 441*a(n-2).

Conjectures from Colin Barker, Jan 20 2019: (Start)

G.f.: 24*x*(1 + 15*x) / (1 - 21*x)^2.

a(n) = 8*3^n * 7^(n-2) * (12*n-5).

(End)

Example

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

Crossrefs

Column 3 of A269276.

Sequence in context: A068294 A003170 A160310 * A347857 A187852 A276595

Adjacent sequences: A269268 A269269 A269270 * A269272 A269273 A269274

Keyword

nonn

Author

R. H. Hardin, Feb 21 2016

Status

approved