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A275166 Number of n-node graphs that have 2 non-isomorphic components. 10
0, 1, 1, 3, 8, 29, 140, 998, 12139, 273400, 11991356, 1018707920, 165078860603, 50500999728875, 29053989521339474, 31426435300576595334, 64000986599534312444935, 245935832697890955733422940, 1787577661113111145804012075034, 24637809007125076355873926288686728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

"Component" means there are no edges from a node of one component to any node of the other component.

Each of the 2 components may be the empty graph with 0 nodes. That means the graph has only one "visible" component in these cases.

Each of the 2 components must be a connected graph (see A001349). (The empty graph has all properties and is a connected graph.)

The graphs of the 2 components must not be the same (not be isomorphic).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..75

FORMULA

G.f.: [A(x)^2 - A(x^2)]/2 where A(x) is the o.g.f. for A001349.

a(n) = A275165(n) if n odd.

EXAMPLE

a(4)=8 = 1*6 + 1*2 where 1*6=A001349(0)*A001349(4) counts graphs with an empty component and a component with 4 nodes, where 1*2 = A001349(1)*A001349(3) counts graphs with a component of 1 node and a component of 3 nodes. There is no contribution from a component of 2 nodes and another component of 2 nodes (both components were isomorphic in that case).

CROSSREFS

Cf. A216785, A001349, A275165.

Sequence in context: A063839 A192744 A130470 * A182117 A207828 A208678

Adjacent sequences:  A275163 A275164 A275165 * A275167 A275168 A275169

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 18 2016

STATUS

approved

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Last modified October 23 03:37 EDT 2018. Contains 316519 sequences. (Running on oeis4.)