A183615 1/120 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock containing four distinct values.

6, 56, 528, 4992, 47232, 446976, 4230144, 40034304, 378888192, 3585835008, 33936703488, 321180401664, 3039683936256, 28767877595136, 272262116671488, 2576716337774592, 24386305253179392, 230794470931562496

Offset

1,1

Comments

Column 2 of A183622.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 12*a(n-1)-24*a(n-2).

Conjecture: G.f.: 1/(x*(3- G(0))) -1/x, where G(k)= 1 + 2^k/(1 - 2*x/(2*x + 2^k*1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 21 2013

Example

Some solutions with the first square being 0123 for 5 X 3
..0..1..0....0..1..2....0..1..2....0..1..4....0..1..4....0..1..4....0..1..4
..2..3..2....2..3..0....2..3..0....2..3..2....2..3..2....2..3..2....2..3..2
..0..4..0....0..4..2....0..1..2....4..1..4....0..1..0....1..0..1....4..1..4
..1..3..1....1..3..0....4..3..4....0..3..0....4..3..4....3..4..3....2..0..3
..2..0..4....0..2..1....0..1..2....4..1..2....0..1..2....1..0..2....1..4..1

Crossrefs

Sequence in context: A155613 A183586 A166177 * A181589 A093142 A092655

Adjacent sequences: A183612 A183613 A183614 * A183616 A183617 A183618

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved