# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a005142 Showing 1-1 of 1 %I A005142 M2501 #53 Feb 20 2023 22:08:38 %S A005142 1,1,1,1,3,5,17,44,182,730,4032,25598,212780,2241730,31193324, %T A005142 575252112,14218209962,472740425319,21208887576786,1286099113807999, %U A005142 105567921675718772,11743905783670560579,1772771666309380358809,363526952035325887859823,101386021137641794979558045 %N A005142 Number of connected bipartite graphs with n nodes. %C A005142 Also, the number of unlabeled connected bicolored graphs having n nodes; the color classes may be interchanged. - _Robert W. Robinson_ %C A005142 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). %C A005142 Also, first diagonal of triangle in A126736. %C A005142 EULER transform of [1, 1, 1, 3, 5, 17, ...] is A033995 [1, 2, 3, 7, 13, ...]. - _Michael Somos_, May 13 2019 %D A005142 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998. %D A005142 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976. %D A005142 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005142 Andrew Howroyd, Table of n, a(n) for n = 0..50 %H A005142 Jean-François Alcover, Mathematica program %H A005142 Keith M. Briggs, Combinatorial Graph Theory %H A005142 CombOS - Combinatorial Object Server, Generate graphs %H A005142 P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57. %H A005142 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.) %H A005142 Eric Weisstein's World of Mathematics, Bipartite Graph. %H A005142 Eric Weisstein's World of Mathematics, n-Chromatic Graph %H A005142 Eric Weisstein's World of Mathematics, n-Colorable Graph %H A005142 Jonathan Wurtz and Danylo Lykov, The fixed angle conjecture for QAOA on regular MaxCut graphs, arXiv:2107.00677 [quant-ph], 2021. %F A005142 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 %t A005142 (* See the links section. *) %Y A005142 Cf. A033995, A116079, A318869, A318870. %K A005142 nonn,nice %O A005142 0,5 %A A005142 _N. J. A. Sloane_ %E A005142 More terms from Ronald C. Read. %E A005142 a(0)=1 prepended by _Max Alekseyev_, Jun 24 2013 %E A005142 Terms a(21) and beyond from _Andrew Howroyd_, Sep 04 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE