A166808 Number of n X 5 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 nondecreasing order.

4, 19, 54, 124, 250, 460, 790, 1285, 2000, 3001, 4366, 6186, 8566, 11626, 15502, 20347, 26332, 33647, 42502, 53128, 65778, 80728, 98278, 118753, 142504, 169909, 201374, 237334, 278254, 324630, 376990, 435895, 501940, 575755, 658006, 749396, 850666, 962596

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = binomial(n+5,5) - 2. - Jeffrey Shallit, May 30 2012

From G. C. Greubel, May 24 2016: (Start)

G.f.: 1/(1-x)^6 - (1+x)/(1-x).

E.g.f.: (1/5!)*(x^5 + 25*x^4 + 200*x^3 + 600*x^2 + 600*x -120)*exp(x) +1. (End)

Example

Some solutions for n=4
...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...1.1.1.1.2
...1.1.1.1.1...1.1.1.1.1...1.1.1.1.2...1.1.1.2.2...1.1.1.2.2...1.1.1.1.2
...1.1.2.2.2...1.1.1.2.2...1.1.1.2.2...2.2.2.2.2...1.1.2.2.2...1.1.1.2.2
...1.1.2.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...1.1.2.2.2...1.1.1.2.2
------
...1.1.1.1.1...1.1.1.1.2...1.1.1.2.2...1.1.1.2.2...1.2.2.2.2...1.1.1.2.2
...1.1.1.2.2...1.1.1.1.2...1.1.2.2.2...2.2.2.2.2...1.2.2.2.2...1.1.1.2.2
...1.1.1.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...2.2.2.2.2...2.2.2.2.2
...2.2.2.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...2.2.2.2.2...2.2.2.2.2

Mathematica

Table[Binomial[n+5, 5] -2, {n, 1, 100}] (* G. C. Greubel, May 24 2016 *)

Crossrefs

Sequence in context: A304993 A171354 A159833 * A253008 A186310 A122684

Adjacent sequences: A166805 A166806 A166807 * A166809 A166810 A166811

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved