A166797 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 nondecreasing order.

0, 8, 67, 269, 776, 1846, 3863, 7371, 13112, 22068, 35507, 55033, 82640, 120770, 172375, 240983, 330768, 446624, 594243, 780197, 1012024, 1298318, 1648823, 2074531, 2587784, 3202380, 3933683, 4798737, 5816384, 7007386, 8394551

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 + 115*n^4 + 90*n^3 - 746*n^2 + 702*n - 180) /180.

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

Empirical G.f.: -x^2*(x^5 + 2*x^4 - 20*x^3 + 32*x^2 - 11*x - 8)/(1-x)^7.

Empirical E.g.f.: (1/180)*(-180 + 180*x + 630*x^2 + 1320*x^3 + 360*x^4 + 33*x^5 + x^6)*exp(x) + 1. (End)

Example

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

Crossrefs

Sequence in context: A076527 A247112 A166815 * A196453 A343091 A037594

Adjacent sequences: A166794 A166795 A166796 * A166798 A166799 A166800

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved