A000703 Chromatic number (or Heawood number) of nonorientable surface with n crosscaps.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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, 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

Crossrefs

Cf. A000934 (the orientable case).

Programs

Haskell

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

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 *)

Formula

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