A166819 Number of nX3 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in increasing order.

1, 14, 83, 308, 877, 2106, 4487, 8744, 15897, 27334, 44891, 70940, 108485, 161266, 233871, 331856, 461873, 631806, 850915, 1129988, 1481501

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

Empirical: a(n)=(n^6+9*n^5+55*n^4+15*n^3-56*n^2+66*n)/90

Example

Some solutions for n=4
...1.1.1...1.1.1...1.1.1...1.3.3...1.2.2...1.1.3...1.1.1...1.1.3...1.1.1
...1.2.2...1.1.2...1.2.3...2.2.3...2.2.3...1.1.3...1.1.2...1.2.2...1.1.2
...2.2.3...1.2.2...1.2.3...2.3.3...2.2.3...2.2.3...1.2.2...2.2.2...1.3.2
...3.3.3...3.3.2...2.2.3...3.3.3...2.2.3...2.3.3...1.3.2...2.2.2...1.3.2
------
...1.2.3...1.1.1...1.2.2...1.1.3...1.2.3...1.1.2...1.1.1...1.1.1...1.1.2
...1.2.3...1.1.3...1.2.2...1.2.3...1.2.3...2.2.2...1.2.3...1.2.2...1.2.2
...1.2.3...2.2.3...1.2.2...1.3.3...1.3.3...2.3.2...1.2.3...1.2.3...1.3.2
...2.2.3...2.3.3...2.2.3...1.3.3...1.3.3...3.3.3...3.3.3...3.3.3...3.3.2

Crossrefs

Sequence in context: A374650 A176010 A250562 * A108683 A376290 A323415

Adjacent sequences: A166816 A166817 A166818 * A166820 A166821 A166822

Keyword

nonn

Author

R. H. Hardin Oct 21 2009

Status

approved