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A070166
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Triangle read by rows giving T(n,k) = number of rooted graphs on n nodes with k edges (n >= 1, 0 <= k <= n(n-1)/2).
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1
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1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 6, 4, 2, 1, 1, 2, 5, 11, 17, 18, 17, 11, 5, 2, 1, 1, 2, 5, 13, 29, 52, 76, 94, 94, 76, 52, 29, 13, 5, 2, 1, 1, 2, 5, 14, 35, 83, 173, 308, 487, 666, 774, 774, 666, 487, 308, 173, 83, 35, 14, 5, 2, 1, 1, 2, 5, 14, 37, 98, 252, 585, 1239, 2396, 4135, 6340
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| T(n,k) is also the number of graphs with n-1 nodes and k edges which may contain loops. (Delete the root node and change every edge leading to it into a loop.)
T(n,k) is also the number of symmetric relations with n-1 points and k relations.
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LINKS
| Eric Weisstein's World of Mathematics, Rooted Graphs
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EXAMPLE
| Triangle begins 1; 1,1; 1,2,2,1; 1,2,4,6,4,2,1; 1,2,5,11,17,18,17,11,5,2,1; ... (the last batch giving either the numbers of rooted graphs on 5 nodes, or the numbers of graphs with loops on 4 nodes; with from 0 to 10 edges).
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CROSSREFS
| Cf. A000666.
Sequence in context: A081372 A101489 A104156 * A131373 A034853 A110283
Adjacent sequences: A070163 A070164 A070165 * A070167 A070168 A070169
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KEYWORD
| nonn,tabf,nice
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs) and Eric Weisstein (eric(AT)weisstein.com), Apr 23, 2002
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