A166820 Number of nX3 1..4 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, 51, 586, 3372, 13564, 43626, 120168, 295100, 662914, 1386373, 2733412, 5128640

Offset

1,2

Links

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

Formula

From G. C. Greubel, May 25 2016: (Start)

Empirical: a(n) = (2/9!)*n*(n-1)*(495648 - 321048*n + 303248*n^2 + 269228*n^3 + 65759*n^4 + 9815*n^5 + 569*n^6 + 29*n^7).

Empirical G.f.: x^2*(51 + 76*x - 193*x^2 + 94*x^3 + 116*x^4 - 144*x^5 + 68*x^6 - 10*x^7)/(1 - x)^10.

Empirical E.g.f.: (2/9!)*x^2*(4626720 + 13093920*x + 10085040*x^2 + 3105648*x^3 + 470484*x^4 + 37764*x^5 + 1584*x^6 + 29*x^7)*exp(x). (End)

Example

Some solutions for n=4
...1.4.4...1.1.4...1.1.1...1.2.2...1.1.2...1.2.3...2.4.4...1.4.4...1.1.2
...1.4.4...3.4.4...1.1.3...2.2.2...1.4.2...2.2.3...3.1.1...2.2.4...1.2.2
...3.2.4...3.4.4...2.3.3...3.2.4...1.4.2...2.4.3...3.1.3...3.2.4...2.2.2
...3.3.3...4.4.2...4.3.3...3.2.4...3.4.2...4.4.4...3.3.3...3.4.4...4.3.2
------
...1.1.1...1.1.2...2.2.3...1.2.2...1.2.2...1.1.4...1.4.4...1.1.4...1.1.1
...1.2.3...3.3.3...2.3.3...1.2.4...2.2.4...1.1.4...2.3.4...1.2.4...1.1.1
...1.2.3...3.3.4...2.3.3...2.2.3...2.2.4...1.3.2...3.3.4...3.2.3...1.4.4
...4.2.2...3.4.4...4.3.1...2.3.3...3.3.3...1.3.2...4.4.4...3.3.3...2.3.4

Crossrefs

Sequence in context: A251932 A319542 A173804 * A269438 A269622 A210055

Adjacent sequences: A166817 A166818 A166819 * A166821 A166822 A166823

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved