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

0,3

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

Links

Table of n, a(n) for n=0..100.

Wikipedia, Four color theorem

Wolfram Mathworld, Four-Color Theorem

Index entries for linear recurrences with constant coefficients, signature (1).

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.: prod(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

Prog

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

Crossrefs

Cf. A000934, A291041.

Cf. A130130. - Jaume Oliver Lafont, Mar 20 2009

Sequence in context: A368420 A193669 A065686 * A065680 A093391 A210964

Adjacent sequences: A158408 A158409 A158410 * A158412 A158413 A158414

Keyword

nonn,easy

Author

Jaume Oliver Lafont, Mar 18 2009

Status

approved