The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135919 Chromatic number of stage-n Menger sponge. 1
4, 11, 34, 133, 566, 2488, 11056, 49323, 220373, 985176, 4405203, 19699535, 88096982, 393978082, 1761917118, 7879521402, 35238270419, 157590299379, 704765178272, 3151805575994, 14095302829230, 63036110202947 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000934(A135918(n)).
LINKS
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
Sequence in context: A149234 A149235 A149236 * A034755 A297608 A034756
KEYWORD
easy,nonn
AUTHOR
Marc LeBrun, Dec 05 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)