A166782 Number of n X 3 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.

6, 90, 454, 1541, 4186, 9808, 20646, 40039, 72750, 125334, 206550, 327817, 503714, 752524, 1096822, 1564107, 2187478, 3006354, 4067238, 5424525, 7141354, 9290504

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Formula

Empirical: a(n) = (11*n^6 + 57*n^5 + 545*n^4 + 285*n^3 + 1424*n^2 - 1782*n + 540)/180.

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

Empirical G.f.: x*(3*x^6 + x^5 - 7*x^4 + 43*x^3 - 50*x^2 + 48*x + 6 ) ) / (1-x)^7.

Empirical E.g.f.: (1/180)*(540 + 540*x + 7290*x^2 + 5970*x^3 + 1830*x^4 + 222*x^5 + 11*x^6)*exp(x) - 3. (End)

Example

Some solutions for n=4:
...2.1.1...1.1.1...2.1.1...3.1.1...2.1.1...3.2.1...1.2.2...2.2.2...1.1.1
...2.2.2...1.1.1...3.3.1...3.1.1...2.2.2...3.2.1...3.2.3...3.2.1...1.1.1
...3.2.2...1.1.3...3.3.3...3.1.1...2.2.2...3.2.1...3.3.3...3.3.1...2.3.1
...3.3.2...1.2.2...3.3.3...3.2.1...3.3.2...3.3.3...3.3.3...3.3.1...3.3.3
------
...1.1.1...2.2.1...1.2.2...1.3.2...3.1.1...1.1.1...3.1.1...1.2.3...1.1.2
...3.2.1...2.2.2...2.2.2...1.3.2...3.2.2...1.1.3...3.1.1...1.2.3...1.1.3
...3.3.1...3.3.2...2.3.3...1.3.3...3.3.2...2.2.3...3.2.1...1.2.3...3.3.3
...3.3.1...3.3.3...3.3.3...1.3.3...3.3.3...2.2.3...3.2.2...1.3.3...3.3.3

Crossrefs

Sequence in context: A100297 A177568 A177573 * A121249 A113404 A177283

Adjacent sequences: A166779 A166780 A166781 * A166783 A166784 A166785

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved