A232950 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

9, 129, 1881, 27441, 400329, 5840289, 85202361, 1242993681, 18133691049, 264547403649, 3859408908441, 56303849204721, 821401284620169, 11983196174074209, 174819534903392121, 2550393846506436561

Offset

1,1

Links

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

Formula

Empirical: a(n) = 15*a(n-1) - 6*a(n-2).

Conjectures from Colin Barker, Oct 06 2018: (Start)

G.f.: 3*x*(3 - 2*x) / (1 - 15*x + 6*x^2).

a(n) = (2^(-1-n)*((15-sqrt(201))^n*(-3+sqrt(201)) + (3+sqrt(201))*(15+sqrt(201))^n)) / sqrt(201).

(End)

Example

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

Crossrefs

Column 3 of A232955.

Sequence in context: A203425 A275259 A064746 * A184143 A287690 A075762

Adjacent sequences: A232947 A232948 A232949 * A232951 A232952 A232953

Keyword

nonn

Author

R. H. Hardin, Dec 02 2013

Status

approved