A166758 Number of nX2 1..5 arrays containing at least one of each value, and all equal values connected.

0, 0, 840, 13320, 99720, 495720, 1889760, 5967360, 16358640, 40158000, 90215640, 188431320, 370311480, 691081560, 1233676080, 2118959760, 3518563680, 5670751200, 8899759080, 13639089960, 20459263080, 30100560840, 43511339520

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n=1..28

Formula

Empirical: a(n) = (1/21)*(n-1)*(n-2)*(16*n^6 - 80*n^5 + 512*n^4 - 1720*n^3 + 3525*n^2 - 4227*n + 2520).

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

Empirical G.f.: 120*x^3*(2*x^6 + 12*x^5 + 43*x^4 + 60*x^3 + 84*x^2 +48*x + 7 ) / (1-x)^9.

Empirical E.g.f.: (1/21)*(5040 - 5040*x + 2520*x^2 + 2100*x^3 + 8925*x^4 + 7224*x^5 + 2352*x^6 + 320*x^7 + 16*x^8)*exp(x) - 240. (End)

Example

Some solutions for n=3
...4.3...4.5...1.1...2.3...2.2...4.3...1.1...2.5...1.3...5.3...3.4...4.5...5.4
...1.5...4.2...5.2...1.3...5.4...5.1...2.4...3.3...4.5...4.1...5.1...1.1...1.1
...1.2...1.3...3.4...5.4...1.3...2.2...3.5...1.4...2.2...2.1...5.2...2.3...2.3
------
...1.2...1.4...1.5...3.5...4.1...1.2...1.2...4.1...1.2...5.5...3.1...1.3...5.1
...3.4...1.2...4.4...2.4...3.5...5.2...3.4...2.3...3.5...2.3...3.2...4.4...4.2
...5.4...5.3...2.3...2.1...2.2...3.4...3.5...5.5...4.5...1.4...5.4...5.2...3.3

Crossrefs

Sequence in context: A135038 A215230 A171260 * A188781 A166764 A226268

Adjacent sequences: A166755 A166756 A166757 * A166759 A166760 A166761

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved