A166801 Number of nX3 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.

1, 26, 134, 443, 1163, 2636, 5384, 10165, 18037, 30430, 49226, 76847, 116351, 171536, 247052, 348521, 482665, 657442, 882190, 1167779, 1526771

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

Empirical: a(n) = (n^6 + 9*n^5 + 70*n^4 + 135*n^3 +64*n^2 -279*n +90)/90.

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

Empirical G.f.: x*(x^6 - 3*x^5 + x^4 + 16*x^3 - 27*x^2 +19*x +1)/(1-x)^7.

Empirical E.g.f.: (1/90)*(90 + 1125*x^2 + 870*x^3 + 225*x^4 + 24*x^5 + x^6)*exp(x) - 1. (End)

Example

Some solutions for n=4
...1.1.1...1.1.2...1.2.2...1.1.3...1.1.1...1.1.1...1.2.2...1.1.3...1.2.3
...1.1.1...2.2.2...1.2.2...2.2.3...1.1.1...1.1.2...1.2.2...1.3.3...3.3.3
...1.1.3...2.3.2...3.3.3...2.2.3...1.1.3...2.2.2...2.2.2...2.2.3...3.3.3
...1.2.3...3.3.3...3.3.3...2.2.3...2.2.2...2.2.3...3.3.3...3.3.3...3.3.3
------
...1.3.3...1.1.1...1.1.1...1.1.3...1.1.1...1.1.2...1.2.2...1.1.2...1.1.3
...1.3.3...1.1.3...1.2.2...1.2.2...1.2.2...1.2.2...1.2.3...2.2.2...1.2.3
...2.2.3...1.2.3...1.2.3...2.2.2...2.2.3...1.2.2...2.2.2...2.2.2...1.3.3
...2.3.3...1.2.3...2.2.3...2.2.2...3.3.3...3.3.3...2.2.2...2.3.3...3.3.3

Crossrefs

Sequence in context: A042316 A042318 A264287 * A255019 A223418 A331458

Adjacent sequences: A166798 A166799 A166800 * A166802 A166803 A166804

Keyword

nonn,more

Author

R. H. Hardin, Oct 21 2009

Status

approved