0,1

a(0) = 4 is the celebrated four-color theorem.

"In 1890 P. Heawood discovered the formula ... and proved that the number of colors required to color a map on an n-holed torus (n =>1) is at most Chi(n). In 1968 G. Ringel and J. W. T. Youngs succeeded in showing that for every n>=1, there is a configuration of Chi(n) countries on an n-holed torus such that each country shares a border with each of the Chi(n)-1 other countries; this shows that Chi(n) colors may be necessary. This completed the proof that Heawood's formula is indeed the correct chromatic number function for the n-holed torus." ... "Heawood's formula is in fact valid for n = 0." - Stan Wagon.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

K. Appel and W. Haken, Every planar map is four colorable. I. Discharging. Illinois J. Math. 21 (1977), 429-490.

K. Appel and W. Haken, Every planar map is four colorable. II. Reducibility. Illinois J. Math. 21 (1977), 491-567.

K. Appel and W. Haken, Every planar map is four colorable. With the collaboration of J. Koch. Contemporary Mathematics, 98. American Mathematical Society, Providence, RI, 1989. xvi+741 pp. ISBN: 0-8218-5103-9.

K. Appel and W. Haken, "The Four-Color Problem" in Mathematics Today (L. A. Steen editor), Springer NY 1978.

K. Appel and W. Haken, "The Four-Color proof suffices", Mathematical Intelligencer 8 no.1 pp. 10-20 1986.

K. Appel and W. Haken, "The Solution of the Four-Color Map Problem", Scientific American vol. 237 no.4 pp. 108-121 1977.

D. Barnett, Map coloring, Polyhedra and The Four-Color Problem, Dolciani Math. Expositions No. 8, Math. Asso. of Amer., Washington DC 1984.

J. H. Cadwell, Topics in Recreational Mathematics, Chapter 8 pp. 76-87 Cambridge Univ. Press 1966.

K. J. Devlin, All The Math That's Fit To Print, Chap. 17; 67 pp. 46-8; 161-2 MAA Washington DC 1994.

K. J. Devlin, Mathematics: The New Golden Age, Chapter 7, Columbia Univ. Press NY 1999.

M. Gardner, New Mathematical Diversions, Chapter 10 pp. 113-123, Math. Assoc. of Amer. Washington DC 1995.

J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see Table 5.1 p. 221.

M. E. Lines, Think of a Number, Chapter 10 pp. 91-100 Institute of Physics Pub. London 1990.

G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem, Proc. Nat. Acad. Sci. USA, 60 (1968), 438-445.

Robertson, N.; Sanders, D.; Seymour, P. and Thomas, R., The four-color theorem. J. Combin. Theory Ser. B 70 (1997), no. 1, 2-44.

Robertson, N.; Sanders, D. P.; Seymour, P. and Thomas, R., A new proof of the four-color theorem. Electron. Res. Announc. Amer. Math. Soc. 2 (1996), no. 1, 17-25.

W. W. Rouse Ball & H. S. M. Coxeter, Mathematical Recreations and Essays, Chapter VIII pp. 222-242 Dover NY 1987.

W. L. Schaaf, Recreational Mathematics. A guide to the literature, Chapter 4.7 pp. 74-6 NCTM Washington DC 1963.

W. L. Schaaf, A Bibliography of Recreational Mathematics Vol. 2, Chapter 4.6 pp. 75-9 NCTM Washington DC 1972.

I. Stewart, From Here to Infinity, Chapter 8 pp. 104-112, Oxford Univ.Press 1996.

H. Tietze, Famous Problems of Mathematics, Chapter XI pp. 226-242 Graylock Press Baltimore MD 1966.

Stan Wagon, Mathematica In Action, W.H. Freeman and Company, NY, 1991, pages 232 - 237.

R. Wilson, Four Colors Suffice, Princeton Univ. Press, 2002.

T. D. Noe, Table of n, a(n) for n=0..1000

P. Alfeld, The Four Color Map Problem

K. Devlin, Last doubts removed about the proof of the Four Color Theorem

P. D\"orre, Every planar map is 4-color and 5-choosable

R. E. Kenyon, Jr., Toward an Inductive Solution for the Four Color Problem

C. Lozier, The Four Color Theorem

MegaMath, Four Color Theorem

J. J. O'Connor & E. F. Robertson, The four color theorem

G. Ringel & J. W. T. Youngs, Solution Of The Heawood Map-Coloring Problem

N. Robertson et al., The Four Color Theorem

D. S. Silver, Map Quest : Review of "Four Colors Suffice" by R.Wilson

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(n) = floor( (7+sqrt(1+48n))/2 ).

A000934 := n-> floor((7+sqrt(1+48*n))/2);

Table[ Floor[ N[(7 + Sqrt[48n + 1])/2] ], {n, 0, 100} ]

Sequence in context: A090383 A082390 A011517 this_sequence A004710 A060257 A161986

Adjacent sequences: A000931 A000932 A000933 this_sequence A000935 A000936 A000937

easy,nice,nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 08 2000