A135919 Chromatic number of stage-n Menger sponge.

4, 11, 34, 133, 566, 2488, 11056, 49323, 220373, 985176, 4405203, 19699535, 88096982, 393978082, 1761917118, 7879521402, 35238270419, 157590299379, 704765178272, 3151805575994, 14095302829230, 63036110202947

Offset

0,1

Comments

a(n) = A000934(A135918(n)).

Links

Table of n, a(n) for n=0..21.

C. Mackeprang & K. Myers, Coloring Graphs on Sponges: Problem 11208, Amer. Math. Monthly 114 (November 2007), p. 842.

Formula

a(n) = floor((7 + sqrt(1 + 48*(21*20^n + 38*8^n - 59)/133))/2).

Example

a(0)=4 because a cube requires at most 4 colors. a(1)=11 because a cube with holes drilled through the faces meeting in the center requires at most 11 colors.

Mathematica

Table[Floor[(7+Sqrt[1+48*(21*20^n+38*8^n-59)/133])/2], {n, 0, 30}] (* Harvey P. Dale, Mar 07 2012 *)

Crossrefs

Cf. A000934, A135918.

Sequence in context: A149234 A149235 A149236 * A034755 A297608 A034756

Adjacent sequences: A135916 A135917 A135918 * A135920 A135921 A135922

Keyword

easy,nonn

Author

Marc LeBrun, Dec 05 2007

Status

approved