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Search: id:A135919
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| A135919 |
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Chromatic number of stage-n Menger sponge. |
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+0
2
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| 4, 11, 34, 133, 566, 2488, 11056, 49323, 220373, 985176, 4405203, 19699535, 88096982, 393978082, 1761917118, 7879521402, 35238270419, 157590299379, 704765178272, 3151805575994, 14095302829230, 63036110202947
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = A000934(A135918(n))
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REFERENCES
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C. Mackeprang & K. Myers, Coloring Graphs on Sponges, Problem 11208, Amer. Math. Monthly 114 (November 2007), solutions p. 842.
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FORMULA
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floor((7 + sqrt(1 + 48*(21*20^n + 38*8^n - 59)/133))/2)
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000934, A135918.
Sequence in context: A149234 A149235 A149236 this_sequence A034755 A034756 A029853
Adjacent sequences: A135916 A135917 A135918 this_sequence A135920 A135921 A135922
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Dec 05 2007
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