

A068933


Triangular array D(n, r) = number of disconnected rregular graphs with n nodes, 0 <= r < n.


18



0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 1, 1, 4, 2, 1, 0, 0, 0, 0, 0, 1, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 8, 9, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 9, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 12, 31, 25, 3, 1, 0, 0, 0, 0, 0
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OFFSET

1,31


COMMENTS

A graph is called rregular if every node has exactly r edges. Row sums give A068932.


LINKS

Jason Kimberley, Rows 1..23 of A068933 triangle, flattened.
Jason Kimberley, Disconnected regular graphs (with girth at least 3)
Jason Kimberley, Index of sequences counting disconnected kregular simple graphs with girth at least g


FORMULA

D(n, r) = A051031(n, r)  A068934(n, r).


EXAMPLE

This sequence can be computed using the information in A068934. We'll abbreviate A068934(n, r) as C(n, r). To compute D(13, 4), note that the connected components of a 4regular graph must have at least 5 elements. So a disconnected 13node 4regular graph must have two components and their sizes are either 8 and 5, or 7 and 6. So D(13, 4) = C(8, 4)*C(5, 4) + C(7, 4)*C(6, 4) = 6*1 + 2*1 = 8.
0;
1, 0;
1, 0, 0;
1, 1, 0, 0;
1, 0, 0, 0, 0;
1, 1, 1, 0, 0, 0;
1, 0, 1, 0, 0, 0, 0;
1, 1, 2, 1, 0, 0, 0, 0;
1, 0, 3, 0, 0, 0, 0, 0, 0;
1, 1, 4, 2, 1, 0, 0, 0, 0, 0;
1, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0;
1, 1, 8, 9, 3, 1, 0, 0, 0, 0, 0, 0;
1, 0, 9, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0;
1, 1, 12, 31, 25, 3...


CROSSREFS

Cf. A051031, A068932, A068934.
Sequence in context: A321921 A236419 A114448 * A015472 A049816 A328958
Adjacent sequences: A068930 A068931 A068932 * A068934 A068935 A068936


KEYWORD

nonn,tabl


AUTHOR

David Wasserman, Mar 08 2002


STATUS

approved



