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 A309524 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with longest path having k nodes, (1 <= k <= n). 2
 1, 0, 1, 0, 0, 2, 0, 0, 1, 5, 0, 0, 1, 2, 18, 0, 0, 1, 3, 17, 91, 0, 0, 1, 3, 29, 86, 734, 0, 0, 1, 4, 42, 176, 864, 10030, 0, 0, 1, 4, 64, 309, 2032, 10243, 248427 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Paths here are subgraphs that are isomorphic to a path graph and are measured by the number of vertices they contain rather than the number of edges. No vertex can appear more than once. Paths with three vertices exist in all connected graphs with at least three vertices. For n > 3, the star graph is the only graph in which longer paths are not possible. LINKS Eric Weisstein's World of Mathematics, Longest Path Eric Weisstein's World of Mathematics, Traceable Graph EXAMPLE Triangle begins:   1;   0, 1;   0, 0, 2;   0, 0, 1, 5;   0, 0, 1, 2, 18;   0, 0, 1, 3, 17,  91;   0, 0, 1, 3, 29,  86,  734;   0, 0, 1, 4, 42, 176,  864, 10030;   0, 0, 1, 4, 64, 309, 2032, 10243, 248427;   ... CROSSREFS Row sums are A001349. Right diagonal is A057864. Cf. A325455 (circumference = longest cycle). Cf. A307457. Sequence in context: A325667 A067310 A122890 * A331106 A318373 A138497 Adjacent sequences:  A309521 A309522 A309523 * A309525 A309526 A309527 KEYWORD nonn,tabl,more AUTHOR Andrew Howroyd, Sep 06 2019 STATUS approved

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Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)