A166776 Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.

0, 12, 51, 135, 286, 530, 897, 1421, 2140, 3096, 4335, 5907, 7866, 10270, 13181, 16665, 20792, 25636, 31275, 37791, 45270, 53802, 63481, 74405, 86676, 100400, 115687, 132651, 151410, 172086, 194805, 219697, 246896, 276540, 308771, 343735, 381582

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..83

Formula

Empirical: a(n) = (n^4 + 8*n^3 + 8*n^2 - 23*n + 6)/6.

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

Empirical G.f.: x^2*(x^3 - 9*x + 12)/(1-x)^5.

Empirical E.g.f.: (1/6)*(6 - 6*x + 39*x^2 + 14*x^3 + x^4)*exp(x) - 1. (End)

Example

All solutions for n=3
...2.2...2.2...2.2...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
...2.2...3.1...3.1...2.2...2.2...2.2...2.1...2.1...2.1...2.3...2.3...3.1...3.1
...3.1...3.1...3.3...2.3...3.2...3.3...2.3...3.1...3.3...2.3...3.3...3.1...3.3
------
...2.1...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1
...3.3...2.2...2.2...2.2...1.2...1.2...1.2...1.3...1.3...3.2...3.2...3.3...2.2
...3.3...2.3...3.2...3.3...1.3...3.2...3.3...1.3...3.3...3.2...3.3...3.3...2.3
------
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1
...2.2...2.2...2.1...2.1...2.1...2.3...2.3...1.2...1.2...1.2...1.1...1.1...1.3
...3.2...3.3...2.3...3.1...3.3...2.3...3.3...1.3...3.2...3.3...2.3...3.2...2.2
------
...1.1...1.1...1.1...1.1...1.3...1.3...1.3...1.3...1.3...3.1...3.1...3.1
...1.3...3.2...3.2...3.1...2.2...2.3...2.3...1.3...1.3...3.2...3.2...3.1
...2.3...3.2...3.3...3.2...2.2...2.3...3.3...2.2...2.3...3.2...3.3...3.2

Crossrefs

Sequence in context: A349860 A268351 A374384 * A200887 A236770 A334695

Adjacent sequences: A166773 A166774 A166775 * A166777 A166778 A166779

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved