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%I #8 Jun 05 2019 09:21:21
%S 4,11,34,133,566,2488,11056,49323,220373,985176,4405203,19699535,
%T 88096982,393978082,1761917118,7879521402,35238270419,157590299379,
%U 704765178272,3151805575994,14095302829230,63036110202947
%N Chromatic number of stage-n Menger sponge.
%C a(n) = A000934(A135918(n)).
%H C. Mackeprang & K. Myers, <a href="https://www.jstor.org/stable/27642353">Coloring Graphs on Sponges: Problem 11208</a>, Amer. Math. Monthly 114 (November 2007), p. 842.
%F a(n) = floor((7 + sqrt(1 + 48*(21*20^n + 38*8^n - 59)/133))/2).
%e 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.
%t Table[Floor[(7+Sqrt[1+48*(21*20^n+38*8^n-59)/133])/2],{n,0,30}] (* _Harvey P. Dale_, Mar 07 2012 *)
%Y Cf. A000934, A135918.
%K easy,nonn
%O 0,1
%A _Marc LeBrun_, Dec 05 2007