reviewed

approved

proposed

reviewed

editing

proposed

Number of nX3 n X 3 0..4 arrays with no element equal to another within two positions in the same row or column, and new values 0..4 introduced in row major order.

Column 3 of A206359.

Empirical: a(n) = 16*a(n-1) - 20*a(n-2) - 58*a(n-3) + 33*a(n-4) + 30*a(n-5) for n>6.

Empirical g.f.: x*(1 + x - 22*x^2 + 2*x^3 + 69*x^4 + 33*x^5) / ((1 - x)*(1 - 15*x + 5*x^2 + 63*x^3 + 30*x^4)). - Colin Barker, Jun 15 2018

Some solutions for n=4:

Cf. A206359.

R. H. Hardin , Feb 06 2012

approved

editing

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 06 2012

editing

approved

R. H. Hardin, <a href="/A206354/b206354.txt">Table of n, a(n) for n = 1..210</a>

allocated for Ron HardinNumber of nX3 0..4 arrays with no element equal to another within two positions in the same row or column, and new values 0..4 introduced in row major order

1, 17, 230, 3284, 47060, 674564, 9669452, 138605744, 1986829652, 28480003748, 408243662612, 5851926480128, 83883833763260, 1202424123191348, 17236024000927580, 247068000076467824, 3541570646368426820

1,2

Column 3 of A206359

Empirical: a(n) = 16*a(n-1) -20*a(n-2) -58*a(n-3) +33*a(n-4) +30*a(n-5) for n>6

Some solutions for n=4

..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2

..2..0..1....1..0..3....1..0..3....3..2..4....1..3..4....1..2..3....2..3..1

..1..2..3....2..3..4....2..4..0....4..3..1....2..4..3....2..0..4....1..4..0

..3..4..2....3..1..2....4..1..2....2..4..3....3..0..1....3..1..2....3..0..2

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Feb 06 2012

approved

editing

allocated for Ron Hardin

allocated

approved