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 A068933 Triangular array D(n, r) = number of disconnected r-regular 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,31 COMMENTS A graph is called r-regular 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) 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 4-regular graph must have at least 5 elements. So a disconnected 13-node 4-regular 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 A143542 Adjacent sequences:  A068930 A068931 A068932 * A068934 A068935 A068936 KEYWORD nonn,tabl AUTHOR David Wasserman, Mar 08 2002 STATUS approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)