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 A005142 Number of connected bipartite graphs with n nodes. (Formerly M2501) 32
 1, 1, 1, 1, 3, 5, 17, 44, 182, 730, 4032, 25598, 212780, 2241730, 31193324, 575252112, 14218209962, 472740425319, 21208887576786, 1286099113807999, 105567921675718772, 11743905783670560579, 1772771666309380358809, 363526952035325887859823, 101386021137641794979558045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also, the number of unlabeled connected bicolored graphs having n nodes; the color classes may be interchanged. - Robert W. Robinson Also, for n>1, number of connected triangle-free graphs on n nodes with chromatic number 2. - Keith M. Briggs, Mar 21 2006 (cf. A116079). Also, first diagonal of triangle in A126736. EULER transform of [1, 1, 1, 3, 5, 17, ...] is A033995 [1, 2, 3, 7, 13, ...]. - Michael Somos, May 13 2019 REFERENCES R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998. R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 Jean-François Alcover, Mathematica program Keith M. Briggs, Combinatorial Graph Theory CombOS - Combinatorial Object Server, Generate graphs P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57. Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.) Eric Weisstein's World of Mathematics, Bipartite Graph. Eric Weisstein's World of Mathematics, n-Chromatic Graph Eric Weisstein's World of Mathematics, n-Colorable Graph Jonathan Wurtz and Danylo Lykov, The fixed angle conjecture for QAOA on regular MaxCut graphs, arXiv:2107.00677 [quant-ph], 2021. FORMULA a(2*n+1) = A318870(2*n+1)/2, a(2*n) = (a(n) + A318869(n) + A318870(2*n) - A318870(n))/2. - Andrew Howroyd, Sep 04 2018 MATHEMATICA (* See the links section. *) CROSSREFS Cf. A033995, A116079, A318869, A318870. Sequence in context: A001572 A236458 A131342 * A165452 A106063 A215106 Adjacent sequences:  A005139 A005140 A005141 * A005143 A005144 A005145 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from R. C. Read (rcread(AT)math.uwaterloo.ca). a(0)=1 prepended by Max Alekseyev, Jun 24 2013 Terms a(21) and beyond from Andrew Howroyd, Sep 04 2018 STATUS approved

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)