A166839 Number of nX2 1..5 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, 55, 478, 2166, 7120, 19219, 45316, 96732, 191232, 355575, 628738, 1065922, 1743456, 2764723, 4267240, 6431032, 9488448, 13735575, 19545414, 27382990, 37822576, 51567219, 69470764, 92562580, 122075200

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Formula

Empirical: a(n) = (1/7!)*n*(n-1)*(n-2)*(n^5 + 35*n^4 + 523*n^3 + 3361*n^2 + 4396*n - 14436).

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

Empirical G.f.: x^3*(55 - 17*x - 156*x^2 + 214*x^3 - 107*x^4 + 19*x^5)/(1 - x)^9.

Empirical E.g.f.: (1/7!)*x^3*(46200 + 54180*x + 13692*x^2 + 1358*x^3 + 60*x^4 + x^5)*exp(x). (End)

Example

Some solutions for n=4
...3.2...3.2...3.2...2.1...2.1...3.1...2.1...3.1...2.1...2.1...2.2...1.1...2.2
...4.2...3.5...5.1...3.1...2.1...3.2...4.1...3.2...2.3...2.2...4.1...2.1...3.2
...5.1...4.1...5.4...4.5...3.4...3.4...5.3...3.3...5.4...3.4...5.3...2.4...4.2
...5.5...4.4...5.4...4.5...5.4...5.4...5.3...5.4...5.5...5.4...5.3...5.3...5.1
------
...2.2...1.1...3.1...2.1...4.3...4.2...1.1...2.2...3.2...3.2...4.1...1.1...2.1
...3.1...2.1...3.1...3.3...5.1...4.3...3.1...2.2...4.2...3.2...4.1...3.1...2.2
...4.1...3.4...3.5...3.4...5.2...4.4...4.4...3.1...4.2...3.4...4.3...4.2...2.4
...4.5...5.4...4.2...3.5...5.5...5.1...5.2...4.5...5.1...5.1...5.2...4.5...5.3

Crossrefs

Sequence in context: A129217 A116060 A145054 * A166827 A266035 A241699

Adjacent sequences: A166836 A166837 A166838 * A166840 A166841 A166842

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved