A166783 Number of nX3 1..4 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.

0, 252, 2624, 14259, 55748, 177136, 486512, 1197675, 2705424, 5699396, 11330072, 21443587

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

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

Empirical a(n) = (1/45360)*(n-1)*(226800 - 555696*n + 563760*n^2 + 340780*n^3 + 306823*n^4 + 52219*n^5 + 10513*n^6 + 553*n^7 + 40*n^8).

Empirical G.f.: x^2*(5*x^8 + 6*x^7 - 23*x^6 + 268*x^5 - 649*x^4 + 998*x^3 - 641*x^2 + 104*x + 252)/(1-x)^10. (End)

Example

Some solutions for n=3
...3.1.3...3.1.2...2.2.1...1.1.4...1.2.2...1.1.2...3.3.3...1.1.4...1.4.3
...3.3.3...4.4.4...2.3.1...1.2.2...2.2.4...4.3.2...3.3.3...1.2.4...1.4.3
...4.3.2...4.4.4...4.3.3...3.3.3...2.3.4...4.3.2...4.2.1...1.3.4...2.2.2
------
...3.2.1...2.3.1...2.2.2...1.1.1...2.3.1...1.2.2...1.1.1...1.1.1...1.1.1
...3.2.1...4.4.1...2.3.3...1.3.2...3.3.1...4.4.2...2.3.3...2.2.2...4.3.3
...4.1.1...4.4.1...4.1.1...4.4.4...3.4.1...4.4.3...3.3.4...4.2.3...4.4.2

Crossrefs

Sequence in context: A364687 A172223 A154073 * A104679 A117281 A152466

Adjacent sequences: A166780 A166781 A166782 * A166784 A166785 A166786

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved