A166832 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 nonincreasing order.

0, 49, 574, 3170, 12373, 39110, 106825, 261632, 588256, 1233991, 2443430, 4607306

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) = (1/181440)*n*(n-1)*(-1105344 + 219960*n + 516656*n^2 + 235676*n^3 + 53879*n^4 + 8015*n^5 + 569*n^6 + 29*n^7).

Empirical G.f.: x^2*(49 + 84*x - 365*x^2 + 623*x^3 - 560*x^4 + 302*x^5 - 86*x^6 + 11*x^7)/(1 - x)^10.

Empirical E.g.f.: (1/181440)*x^2*(4445280 + 12912480*x + 8830080*x^2 + 2680776*x^3 + 422604*x^4 + 35964*x^5 + 1584*x^6 + 29*x^7)*exp(x). (End)

Example

Some solutions for n=4
...1.1.1...2.1.1...1.1.1...2.1.1...2.2.1...2.2.1...3.2.1...4.2.1...2.1.1
...2.2.2...2.2.1...2.1.1...2.4.4...3.1.1...4.2.2...3.2.1...4.3.1...2.1.1
...3.3.3...2.3.3...2.3.3...2.4.4...3.1.4...4.3.2...3.3.1...4.3.3...2.3.1
...4.3.3...2.3.4...4.4.4...3.3.3...3.3.4...4.4.2...4.3.3...4.4.4...2.4.4
------
...2.2.1...1.1.1...3.3.2...1.1.1...3.2.1...2.2.1...3.1.1...3.3.1...2.2.1
...2.2.1...4.1.1...4.3.3...3.1.1...3.3.3...3.2.2...3.2.1...4.3.3...4.2.1
...3.3.3...4.3.2...4.3.3...3.3.2...3.3.4...3.4.2...3.2.4...4.4.2...4.3.3
...3.3.4...4.3.2...4.4.1...4.4.4...4.4.4...4.4.4...4.4.4...4.4.4...4.3.3

Crossrefs

Sequence in context: A104935 A110203 A263704 * A299711 A175775 A215117

Adjacent sequences: A166829 A166830 A166831 * A166833 A166834 A166835

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved