A166756 Number of nX2 1..3 arrays containing at least one of each value, and all equal values connected.

0, 24, 174, 642, 1716, 3780, 7314, 12894, 21192, 32976, 49110, 70554, 98364, 133692, 177786, 231990, 297744, 376584, 470142, 580146, 708420, 856884, 1027554, 1222542, 1444056, 1694400, 1975974, 2291274, 2642892, 3033516, 3465930, 3943014, 4467744

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..82

Formula

Empirical: a(n) = 4*n^4 - 8*n^3 + 11*n^2 - 13*n + 6.

From G. C. Greubel, May 26 2016: (Start)

Empirical G.f.: 6*x^2*(x^3 + 2*x^2 + 9*x + 4)/(1 - x)^5.

Empirical E.g.f.: (6 - 6*x + 15*x^2 + 16*x^3 + 4*x^4)*exp(x) - 6. (End)

Example

Some solutions for n=4
...1.1...2.3...1.1...3.2...3.3...2.2...2.2...3.1...2.3...2.3...2.1...3.3...1.1
...1.3...2.1...3.1...2.2...3.1...1.2...2.1...2.1...2.2...2.3...2.1...3.2...2.1
...1.2...2.2...2.1...1.1...3.1...1.1...2.3...1.1...2.1...2.3...1.1...3.1...3.3
...2.2...2.2...1.1...1.1...2.1...3.3...3.3...1.1...1.1...1.1...3.3...1.1...3.3
------
...3.3...1.3...1.2...1.2...3.3...3.1...3.2...3.3...2.1...3.2...1.1...2.2...1.1
...3.1...1.1...1.2...1.3...3.3...3.3...3.3...3.2...1.1...3.3...1.3...2.1...2.2
...1.1...1.2...1.1...3.3...1.1...3.3...3.3...2.2...3.1...3.3...1.1...2.2...2.2
...2.1...2.2...3.1...3.3...2.1...2.2...1.1...2.1...1.1...1.3...2.2...3.2...2.3

Crossrefs

Sequence in context: A223291 A221069 A272125 * A268623 A209716 A209709

Adjacent sequences: A166753 A166754 A166755 * A166757 A166758 A166759

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved