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Search: id:A000206
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| A000206 |
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Even sequences with period 2n.
(Formerly M2372 N0940)
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+0
2
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| 1, 1, 3, 4, 12, 22, 71, 181, 618, 1957, 6966, 24367, 89010, 324766, 1204815, 4482400, 16802826, 63195016, 238711285, 904338163, 3436380192, 13089961012, 49979421837, 191221556269, 733014218506, 2814758323498, 10825986453978
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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"Even" orbits of binary necklaces of length 2n under group D_n X S_2.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665.
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LINKS
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N. J. A. Sloane, Maple code for this and related sequences
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FORMULA
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a(0)=1, a(n)= (A000011(2*n)+A000011(n)+4^(n/2-1)-2^(n/2-1))/2 if n even, a(n)= A000011(2*n)/2 if n odd
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PROGRAM
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(PARI) {A000206(n)=if(n==0, 1, if(n%2==0, (A000011(2*n)+A000011(n)+4^(n/2-1)-2^(n/2-1))/2, A000011(2*n)/2))}
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CROSSREFS
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Cf. A000011, A000013, A000208.
Sequence in context: A075221 A129922 A005221 this_sequence A075223 A071332 A006791
Adjacent sequences: A000203 A000204 A000205 this_sequence A000207 A000208 A000209
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, PARI program and formula from Randall L. Rathbun, Jan 11 2002
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