A166796 Number of nX2 1..3 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, 6, 26, 69, 146, 270, 456, 721, 1084, 1566, 2190, 2981, 3966, 5174, 6636, 8385, 10456, 12886, 15714, 18981, 22730, 27006, 31856, 37329, 43476, 50350, 58006, 66501, 75894, 86246, 97620, 110081, 123696, 138534, 154666, 172165, 191106, 211566, 233624

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..83

Formula

Empirical: a(n) = (n^4 + 8*n^3 + 11*n^2 - 32*n + 12)/12.

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

Empirical G.f.: x^2*(x^3 - x^2 - 4*x + 6)/(1-x)^5.

Empirical E.g.f.: (1/12)*(12 - 12*x + 42*x^2 + 14*x^3 + x^4)*exp(x) - 1. (End)

Example

All solutions for n=3
...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1...1.1
...2.2...2.2...2.2...1.2...1.2...1.2...1.3...1.3...3.2...3.2...3.3...2.2...2.2
...2.3...3.2...3.3...1.3...3.2...3.3...1.3...3.3...3.2...3.3...3.3...2.3...3.3
------
...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.3...1.3...1.3...1.3...1.3
...2.3...2.3...1.2...1.2...1.2...1.1...1.3...1.3...2.2...2.3...2.3...1.3...1.3
...2.3...3.3...1.3...3.2...3.3...2.3...2.2...2.3...2.2...2.3...3.3...2.2...2.3

Crossrefs

Sequence in context: A254527 A190095 A135036 * A001701 A241452 A175898

Adjacent sequences: A166793 A166794 A166795 * A166797 A166798 A166799

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved