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Search: id:A151749
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| A151749 |
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a(0) = 1, a(1) = 3; a(n+2) = (a(n+1)+a(n))/2 if 2 divides (a(n+1)+a(n)), a(n+2) = a(n+1)+a(n) otherwise. |
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+0
2
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| 1, 3, 2, 5, 7, 6, 13, 19, 16, 35, 51, 43, 47, 45, 46, 91, 137, 114, 251, 365, 308, 673, 981, 827, 904, 1731, 2635, 2183, 2409, 2296, 4705, 7001, 5853, 6427, 6140, 12567, 18707, 15637, 17172, 32809, 49981, 41395, 45688, 87083, 132771, 109927, 121349, 115638
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Greene discusses the whole family of sequences defined by a rule of the form a(n) = (Sum_{i=1..k} c_i a(i))/ (Sum_{i=1..k} c_i) if (Sum_{i=1..k} c_i) divides (Sum_{i=1..k} c_i a(i)), a(n) = (Sum_{i=1..k} c_i a(i)) if not, where k and the c_i are nonnegative integers and a(0), ..., a(k-1) are specified initial terms. Many further examples of such sequences could be added to the OEIS!
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REFERENCES
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A. M. Amleh et al., On some difference equations ..., J. Math. Anal. Appl., 223 (1998), 196-215.
J. Greene, The unboundedness of a family of difference equations ..., Fib. Q., 46/47 (2008/2009), 146-152.
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MAPLE
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A151749 := proc(n) option remember; if n <= 1 then 1+2*n; else prev := procname(n-1)+procname(n-2) ; if prev mod 2 = 0 then prev/2 ; else prev; fi; fi; end: seq(A151749(n), n=0..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2009]
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CROSSREFS
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Cf. A069202.
Sequence in context: A108918 A118320 A082334 this_sequence A110338 A013655 A094894
Adjacent sequences: A151746 A151747 A151748 this_sequence A151750 A151751 A151752
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 17 2009
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2009
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