Search: id:A000703
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%I A000703 M3265 N1318
%S A000703 4,6,7,7,8,9,9,10,10,10,11,11,12,12,12,13,13,13,13,14,14,14,15,15,15,15,
%T A000703 16,16,16,16,16,17,17,17,17,18,18,18,18,18,19,19,19,19,19,19,20,20,20,
               20,
%U A000703 20,21,21,21,21,21,21,22,22,22,22,22,22,22,23,23,23,23,23,23,24,24,24,
               24
%N A000703 Chromatic number (or Heawood number) of nonorientable surface with n 
               crosscaps.
%D A000703 K. Appel and W. Haken, Every planar map is four colorable. I. Discharging. 
               Illinois J. Math. 21 (1977), no. 3, 429-490.
%D A000703 G. A. Dirac, Map-color theorems, Canad. J. Math., 4 (1952), 480ff.
%D A000703 J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; 
               see Table 5.2 p. 221.
%D A000703 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 
               2004; p. 368 and 631.
%D A000703 G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem, 
               Proc. Nat. Acad. Sci. USA, 60 (1968), 438-445.
%D A000703 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000703 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000703 T. D. Noe, <a href="b000703.txt">Table of n, a(n) for n=0..1000</a>
%H A000703 G. Ringel & J. W. T. Youngs, <a href="http://www.pnas.org/cgi/reprint/
               60/2/438.pdf">Solution Of The Heawood Map-Coloring Problem</a>
%F A000703 a(n) = floor((7+sqrt(1+24*n))/2).
%Y A000703 Cf. A000934 (the orientable case).
%Y A000703 Sequence in context: A135798 A021218 A019605 this_sequence A011275 A006185 
               A021876
%Y A000703 Adjacent sequences: A000700 A000701 A000702 this_sequence A000704 A000705 
               A000706
%K A000703 nonn,nice
%O A000703 0,1
%A A000703 N. J. A. Sloane (njas(AT)research.att.com).

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