A000703 - OEIS

A000703

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

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, 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

Adjacent sequences: A000700 A000701 A000702 * A000704 A000705 A000706

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved