A166759 Number of nX2 1..6 arrays containing at least one of each value, and all equal values connected.

0, 0, 720, 32400, 434160, 3309120, 17807040, 75294000, 266274720, 819872640, 2259483120, 5685633360, 13259846160, 28992150720, 59970549600, 118213974000, 223381776960

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Formula

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

Empirical a(n) = (2/315)*(n-1)*(n-2)*(32*n^8 - 304*n^7 + 2744*n^6 - 15880*n^5 + 62078*n^4 - 171871*n^3 + 319311*n^2 - 353880*n + 170100).

Empirical G.f.: 720*x^3*(3*x+1)*(x^7 + 8*x^6 + 25*x^5 + 57*x^4 + 63*x^3 + 70*x^2 + 31*x + 1)/(1-x)^11.

Empirical E.g.f.: (2/315)*(340200 - 340200*x + 170100*x^2 - 37800*x^3 + 207900*x^4 + 363825*x^5 + 257670*x^6 + 82800*x^7 + 13320*x^8 + 1040*x^9 + 32*x^10)*exp(x) - 2160. (End)

Example

Some solutions for n=3
...4.1...1.4...2.5...5.2...6.4...4.6...3.6...3.2...3.5...2.6...2.5...1.2...4.1
...6.5...5.2...4.3...3.6...5.3...1.2...4.1...6.5...6.2...4.1...3.1...5.3...6.3
...3.2...6.3...1.6...1.4...2.1...5.3...2.5...1.4...1.4...3.5...6.4...4.6...5.2
------
...3.2...5.3...1.5...5.4...1.6...2.6...1.6...1.3...4.1...6.4...6.4...3.4...3.6
...4.5...4.1...3.6...1.6...4.5...3.4...5.2...2.6...5.6...3.2...1.3...6.2...4.1
...1.6...2.6...2.4...3.2...2.3...5.1...4.3...4.5...2.3...1.5...2.5...1.5...5.2

Crossrefs

Sequence in context: A223857 A003938 A052720 * A181504 A179061 A342074

Adjacent sequences: A166756 A166757 A166758 * A166760 A166761 A166762

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved