

A000703


Chromatic number (or Heawood number) of nonorientable surface with n crosscaps.
(Formerly M3265 N1318)


3



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, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


REFERENCES

J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see Table 5.2 p. 221.
J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 368 and 631.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
K. Appel and W. Haken, Every planar map is four colorable. I. Discharging, Illinois J. Math. 21 (1977), no. 3, 429490.
G. A. Dirac, Mapcolor theorems, Canad. J. Math., 4 (1952), 480ff.
G. Ringel & J. W. T. Youngs, Solution Of The Heawood MapColoring Problem, Proc. Nat. Acad. Sci. USA, 60 (1968), 438445.
Eric Weisstein's World of Mathematics, Chromatic Number
Eric Weisstein's World of Mathematics, Heawood Conjecture


FORMULA

a(n) = floor((7+sqrt(1+24*n))/2).


MAPLE

A000703:=n>floor((7+sqrt(1+24*n))/2): seq(A000703(n), n=0..150); # Wesley Ivan Hurt, Apr 24 2017


MATHEMATICA

Floor[(7+Sqrt[1+24*Range[0, 80]])/2] (* Harvey P. Dale, Feb 03 2012 *)


PROG

(Haskell)
a000703 = floor . (/ 2) . (+ 7) . sqrt . (+ 1) . (* 24) . fromInteger
 Reinhard Zumkeller, Dec 04 2012


CROSSREFS

Cf. A000934 (the orientable case).
Sequence in context: A309606 A288179 A198882 * A266148 A011275 A205684
Adjacent sequences: A000700 A000701 A000702 * A000704 A000705 A000706


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



