A222869 Number of n X 3 0..5 arrays with no element equal to another at a city block distance of exactly two, and new values 0..5 introduced in row major order.

3, 34, 816, 30528, 1186704, 46269792, 1804486896, 70374883968, 2744620159824, 107040185288352, 4174567223411376, 162808121704540608, 6349516746451574544, 247631153111534879712, 9657614971349630726256, 376646983882634909576448

Offset

1,1

Comments

Column 3 of A222871.

Links

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

Formula

Empirical: a(n) = 42*a(n-1) - 117*a(n-2) for n>4.

Conjectures from Colin Barker, Aug 16 2018: (Start)

G.f.: x*(3 - 92*x - 261*x^2 + 234*x^3) / ((1 - 3*x)*(1 - 39*x)).

a(n) = 4*3^(n-1) + 20*39^(n-2) for n>2.

(End)

Example

Some solutions for n=3:
..0..0..1....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..1
..2..2..3....3..3..4....3..3..0....3..4..5....3..1..0....3..4..2....2..3..4
..4..5..5....1..2..5....2..4..1....1..2..3....4..2..5....5..4..0....1..5..5

Crossrefs

Cf. A222871.

Sequence in context: A231850 A109521 A274744 * A069718 A077144 A222778

Adjacent sequences: A222866 A222867 A222868 * A222870 A222871 A222872

Keyword

nonn

Author

R. H. Hardin, Mar 07 2013

Status

approved