A166838 Number of nX2 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 decreasing order.

0, 4, 49, 218, 662, 1626, 3479, 6748, 12156, 20664, 33517, 52294, 78962, 115934, 166131, 233048, 320824, 434316, 579177, 761938, 990094, 1272194, 1617935, 2038260, 2545460, 3153280, 3877029, 4733694, 5742058, 6922822, 8298731, 9894704

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..44

Formula

Empirical: a(n) = (n^6 + 18*n^5 + 100*n^4 - 30*n^3 - 551*n^2 + 462*n)/180.

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

Empirical G.f.: x^2*(4 + 21*x - 41*x^2 + 25*x^3 - 5*x^4)/(1 - x)^7.

Empirical E.g.f.: (1/180)*x^2*(360 + 1110*x + 345*x^2 + 33*x^3 + x^4)*exp(x). (End)

Example

All solutions for n=3
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...2.1...2.1...2.1...2.1
...2.1...2.1...2.2...3.1...3.2...3.2...3.2...3.3...4.2...2.1...2.1...2.2...2.2
...3.4...4.3...4.3...4.2...3.4...4.2...4.4...4.2...4.3...3.4...4.3...3.4...4.3
------
...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
...2.3...2.3...2.3...2.4...2.4...3.1...3.1...3.1...3.3...3.3...3.3...3.4...3.4
...2.4...4.3...4.4...3.3...3.4...3.4...4.1...4.4...3.4...4.3...4.4...3.4...4.4
------
...2.1...2.1...2.1...2.2...2.2...2.2...2.2...2.2...2.2...3.1...3.1...3.1...3.1
...4.1...4.3...4.3...3.1...3.1...3.1...3.2...3.3...4.1...3.1...3.2...3.2...3.2
...4.3...4.3...4.4...3.4...4.1...4.4...4.1...4.1...4.3...4.2...3.4...4.2...4.4
------
...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.3...4.1
...3.3...4.1...4.2...4.2...3.2...3.3...4.1...4.1...4.1...4.2
...4.2...4.2...4.2...4.4...4.1...4.1...4.1...4.4...4.2...4.3

Crossrefs

Sequence in context: A092866 A340662 A041065 * A166826 A295535 A078187

Adjacent sequences: A166835 A166836 A166837 * A166839 A166840 A166841

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved