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A109094
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Length of the longest path (repeated edges not allowed) between two arbitrary, distinct nodes in K_n, the complete graph on n vertices.
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1
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0, 1, 2, 5, 9, 13, 20, 25, 35, 41, 54, 61, 77, 85, 104, 113, 135, 145, 170, 181, 209, 221, 252, 265, 299, 313, 350, 365, 405, 421, 464, 481, 527, 545, 594, 613, 665, 685, 740, 761, 819, 841, 902, 925, 989, 1013, 1080, 1105, 1175, 1201, 1274, 1301, 1377, 1405
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Bisections are essentially A001844 and A014107. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 17 2008
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LINKS
| R. J. Mathar, Comments on this sequence
Eric Weisstein. Complete Graph.
Eric Weisstein. Euler Path.
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FORMULA
| a(1)=0; for odd n>1, a(n)=n*(n-1)/2-1; for even n, a(n)=n*(n-2)/2+1. - Martin Fuller (martin_n_fuller(AT)btinternet.com), R. J. Mathar and Mitch Harris, Dec 06 2007
O.g.f.: x^2*(x^4-2*x^3-x^2-x-1)/((-1+x)^3 *(x+1)^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 17 2008
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EXAMPLE
| a(4) = 5 because the length of the longest path between any two distinct vertices in K_4 is 5.
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CROSSREFS
| Cf. A057979, A128223.
Sequence in context: A038707 A071705 A190713 * A049753 A126326 A070986
Adjacent sequences: A109091 A109092 A109093 * A109095 A109096 A109097
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KEYWORD
| nonn
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AUTHOR
| Ryan Propper (rpropper(AT)stanford.edu), Jun 18 2005
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EXTENSIONS
| More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), R. J. Mathar and Mitch Harris, Dec 06 2007
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