A166814 Number of nX2 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.

0, 6, 25, 66, 140, 260, 441, 700, 1056, 1530, 2145, 2926, 3900, 5096, 6545, 8280, 10336, 12750, 15561, 18810, 22540, 26796, 31625, 37076, 43200, 50050, 57681, 66150, 75516, 85840, 97185, 109616, 123200, 138006, 154105, 171570, 190476, 210900, 232921

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+5*n^2-14*n)/12.

Empirical: G.f.: -x^2*(x-2)*(x-3) / (x-1)^5 . - R. J. Mathar, Nov 23 2015

Example

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

Crossrefs

Sequence in context: A255687 A332698 A096958 * A241170 A245679 A354392

Adjacent sequences: A166811 A166812 A166813 * A166815 A166816 A166817

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved