A158411 Maximum number of colors required to paint a map having n regions.

0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

Jaume Oliver Lafont, Mar 18 2009

Keywords

• nonn
• easy

Comments

The generating function can be arranged to have four zeros at the fourth roots of unity. - Jaume Oliver Lafont, Mar 23 2009

Also, the arithmetic function uhat(n,4,3) as defined in A291041. - Robert Price, Aug 25 2017

Decimal expansion of 1111/90000. - Elmo R. Oliveira, May 06 2024

Links

• Eric Weisstein's World of Mathematics, Four-Color Theorem
• Wikipedia, Four color theorem
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000934, A130130, A291041.

Programs

Mathematica

PadRight[Range[0, 3], 100, 4] (* Paolo Xausa, Aug 22 2024 *)

PARI

a(n)=if(n<4,n,4)

Formula

G.f.: x*(1+x+x^2+x^3)/(1-x).

G.f.: x*(1-x^4)/(1-x)^2. - Jaume Oliver Lafont, Mar 20 2009

G.f.: Product_{k=0..3} (1-I^k*x)*x/(1-x)^2. - Jaume Oliver Lafont, Mar 23 2009

a(n) = A130130(n) + A130130(n-2). - Jaume Oliver Lafont, Mar 24 2009

a(n) = min(n,4). - Wesley Ivan Hurt, Apr 16 2014

E.g.f.: 4*exp(x) - 4 - 3*x - x^2 - x^3/6. - Stefano Spezia, May 19 2024