A166840 Number of n X 2 1..6 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 decreasing order.

0, 0, 30, 728, 5364, 24401, 84279, 242772, 614084, 1407834, 2987248, 5953244, 11262680, 20390851, 35550385, 59981016, 98327320, 157124404, 245414754

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

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

Empirical a(n) = (16/(10)!)*n*(n-1)*(n-2)*(1486980 - 1224297*n - 103903*n^2 + 91114*n^3 + 17630*n^4 + 1342*n^5 + 53*n^6 + n^7).

Empirical G.f.: x^3*(30 + 398*x - 994*x^2 + 487*x^3 + 668*x^4 - 922*x^5 + 416*x^6 - 67*x^7)/(1 - x)^11.

Empirical E.g.f.: (16/(10)!)*x^3*(1134000 + 5745600*x + 3825360*x^2 + 799155*x^3 + 75870*x^4 + 3735*x^5 + 95*x^6 + x^7)*exp(x). (End)

Example

All solutions for n=3
...4.3...4.3...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.1...3.1...3.2
...5.1...5.2...4.2...4.2...4.5...4.6...4.1...4.1...4.5...4.6...5.4...5.2...5.4
...6.2...6.1...5.6...6.5...6.2...5.2...5.6...6.5...6.1...5.1...6.2...6.4...6.1
------
...3.2...4.1...4.1...4.2...4.2...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
...5.1...5.3...5.2...5.3...5.1...3.4...3.4...3.5...3.5...3.6...3.6...4.3...4.3
...6.4...6.2...6.3...6.1...6.3...5.6...6.5...6.4...4.6...5.4...4.5...5.6...6.5
------
...2.1...2.1...2.1...2.1
...4.5...4.6...5.3...5.4
...6.3...5.3...6.4...6.3

Crossrefs

Sequence in context: A180801 A035520 A122186 * A166828 A053509 A273435

Adjacent sequences: A166837 A166838 A166839 * A166841 A166842 A166843

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved