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Search: id:A007679
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| A007679 |
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If n mod 4 = 0 then 2^(n-1)+1 elif n mod 4 = 2 then 2^(n-1)-1 else 2^(n-1).
(Formerly M3359)
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+0
3
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| 1, 1, 4, 9, 16, 31, 64, 129, 256, 511, 1024, 2049, 4096, 8191, 16384, 32769, 65536, 131071, 262144, 524289, 1048576, 2097151, 4194304, 8388609, 16777216, 33554431, 67108864, 134217729, 268435456, 536870911
(list; graph; listen)
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OFFSET
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1,3
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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).
M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 37. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
I. Nemes et al., How to do Monthly problems with your computer, Amer. Math. Monthly, 104 (1997), 505-519.
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FORMULA
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2^(n-1) + cos(n*Pi/2).
Sum 2^k*C(n-k, 2k)*n/(n-k), k = 0..[ n/3 ].
a(n) = A007909(n) + A007910(n).
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MAPLE
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f:=n->2^(n-1)+cos(Pi*n/2);
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CROSSREFS
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Sequence in context: A073141 A093175 A138992 this_sequence A068037 A167188 A014764
Adjacent sequences: A007676 A007677 A007678 this_sequence A007680 A007681 A007682
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy, Simon Plouffe.
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