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Search: id:A059222
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| A059222 |
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Minimal number of disjoint edge-paths into which the graph of the n-ary cube can be partitioned. |
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+0
2
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| 1, 1, 4, 1, 16, 1, 64, 1, 256, 1, 1024, 1, 4096, 1, 16384, 1, 65536, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The formula for this sequence is easily derived from a generalization of Euler's famous "Eulerian Path" theorem (see Theorem 11.2.4 in p. 419 of the reference).
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REFERENCES
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R. A. Brualdi, Introductory Combinatorics, 3rd ed. Prentice-Hall, 1999.
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FORMULA
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a(n) = 1 if n is even and 2^(n-1) if n is odd.
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EXAMPLE
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a(5)=16 because 2^(5-1)=16. Consequently, the minimal number of disjoint edge-paths into which the 5-ary cube can be partitioned is 16.
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CROSSREFS
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Cf. A057979.
Sequence in context: A124029 A056920 A123382 this_sequence A117292 A062780 A094361
Adjacent sequences: A059219 A059220 A059221 this_sequence A059223 A059224 A059225
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KEYWORD
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nonn
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AUTHOR
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Felix Golderg (felixg(AT)tx.technion.ac.il), Jan 19 2001
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