A166757 Number of nX2 1..4 arrays containing at least one of each value, and all equal values connected.

0, 24, 504, 3672, 16272, 53784, 146184, 345240, 733344, 1433880, 2623128, 4543704, 7519536, 11972376, 18439848, 27595032, 40267584, 57466392, 80403768, 110521176, 149516496, 199372824, 262388808, 341210520, 438864864, 558794520, 704894424

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..45

Formula

Empirical: a(n) = (4/15)*(n-1)*(8*n^5 -28*n^4 + 97*n^3 - 218*n^2 + 234*n -90).

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

Empirical G.f.: 24*x^2*(x^5 + 8*x^4 + 13*x^3 + 27*x^2 + 14*x + 1)/(1-x)^7.

Empirical E.g.f.: (4/15)*(90 - 90*x + 90*x^2 + 255*x^3 + 285*x^4 + 84*x^5 + 8*x^6)*exp(x) - 24. (End)

Example

Some solutions for n=4
...2.1...3.1...3.4...2.4...4.1...1.4...2.2...3.1...1.4...3.1...3.1...2.2...1.4
...3.3...1.1...3.4...2.2...1.1...2.2...4.1...1.1...2.4...3.1...3.2...2.1...1.3
...3.4...1.2...3.4...1.1...3.1...3.2...3.1...2.1...2.3...3.3...2.2...2.2...1.2
...4.4...4.4...1.2...3.1...3.2...3.2...3.1...2.4...2.3...2.4...4.2...4.3...1.1
------
...4.3...2.3...4.4...4.4...3.3...3.3...2.4...3.3...1.3...1.3...3.3...4.4...1.2
...1.3...2.2...1.1...3.4...3.1...4.4...1.1...2.1...2.3...4.4...3.4...3.4...4.4
...2.3...4.4...3.2...3.1...4.1...4.1...1.1...2.4...2.3...4.4...1.1...3.4...4.4
...3.3...1.1...3.2...2.2...2.1...2.2...1.3...4.4...4.4...2.4...2.1...2.1...4.3

Crossrefs

Sequence in context: A186863 A004383 A112390 * A289833 A242524 A264956

Adjacent sequences: A166754 A166755 A166756 * A166758 A166759 A166760

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved