A166830 Number of n X 3 1..2 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 nonincreasing order.

2, 8, 18, 33, 54, 82, 118, 163, 218, 284, 362, 453, 558, 678, 814, 967, 1138, 1328, 1538, 1769, 2022, 2298, 2598, 2923, 3274, 3652, 4058, 4493, 4958, 5454, 5982, 6543, 7138, 7768, 8434, 9137, 9878, 10658, 11478, 12339, 13242

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Formula

Empirical: a(n) = (n^3+6*n^2+11*n-6)/6.

a(n) = A167772(n+3,n). - Philippe Deléham, Nov 11 2009

a(n) = A227819(n+6,n+2). - Alois P. Heinz, Sep 22 2013

Empirical: a(n) = floor(A000292(n+1)^3/(A000292(n+1) + 1)^ 2). - Ivan N. Ianakiev, Nov 05 2013

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

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

Empirical E.g.f.: (1/6)*(-6 + 18*x + 9*x^2 + x^3)*exp(x) + 1. (End)

Example

All solutions for n=3
...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
...1.1.1...1.1.1...1.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2
...2.1.1...2.2.1...2.2.2...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2
------
...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.1
...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2...2.2.1...2.2.1...2.2.2
...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2...2.2.1...2.2.2...2.2.2

Mathematica

lst={}; Do[AppendTo[lst, n*(n+1)*(n+2)/6-2], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

Crossrefs

Sequence in context: A190787 A018229 A365265 * A072779 A292764 A198014

Adjacent sequences: A166827 A166828 A166829 * A166831 A166832 A166833

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved