login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
K. Appel and W. Haken, Every planar map is four colorable. I. Discharging, Illinois J. Math. 21 (1977), no. 3, 429-490.
G. A. Dirac, Map-color theorems, Canad. J. Math., 4 (1952), 480ff.
G. Ringel & J. W. T. Youngs, Solution Of The Heawood Map-Coloring Problem, Proc. Nat. Acad. Sci. USA, 60 (1968), 438-445.
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: A288179 A198882 A366727 * A266148 A011275 A205684
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)