login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228892 Triangular array read by rows.  T(n,k) is the number of 2-colored labeled graphs on n nodes with exactly k connected components; n>=1, 1<=k<=n. 0
2, 2, 4, 6, 12, 8, 38, 60, 48, 16, 390, 500, 360, 160, 32, 6062, 6180, 3840, 1680, 480, 64, 134526, 109228, 56280, 22400, 6720, 1344, 128, 4172198, 2673468, 1120784, 384720, 109760, 24192, 3584, 256, 178449270, 89708004, 29975400, 8579424, 2187360, 475776, 80640, 9216, 512, 10508108222, 4108881300 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A 2-colored labeled graph is a simple labeled graph in which each vertex is painted black or white and no two vertices of the same color are connected.

Row sums are A047863.

T(n,k) = A228859(n,k)2^k.

LINKS

Table of n, a(n) for n=1..47.

FORMULA

E.g.f.: A(x)^y where A(x) is the e.g.f. for A047863.

EXAMPLE

2,

2, 4,

6, 12, 8,

38, 60, 48, 16,

390, 500, 360, 160, 32,

6062, 6180, 3840, 1680, 480, 64

MATHEMATICA

nn=6; f[x_, y_]:=Sum[Exp[x 2^n] x^n/n!, {n, 0, nn}]; Map[Select[#, #>0&]&, Map[Table[#[[i]]#[[i]]2^(i-1), {i, 1, Length[#]}][[All, 2]]&, Drop[Range[0, nn]!CoefficientList[Series[f[x, y]^(y/2), {x, 0, nn}], {x, y}], 1]]]//Grid

CROSSREFS

Sequence in context: A278246 A195204 A318847 * A267610 A291365 A154779

Adjacent sequences:  A228889 A228890 A228891 * A228893 A228894 A228895

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Sep 07 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 11:09 EST 2019. Contains 329319 sequences. (Running on oeis4.)