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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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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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MAPLE
| 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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MATHEMATICA
| f[{a_, b_}]:=Module[{c=a+b}, If[EvenQ[c], c/2, c]]; Transpose[NestList[ {Last[#], f[#]}&, {1, 3}, 50]][[1]] (* From Harvey P. Dale, Oct 12 2011 *)
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CROSSREFS
| Cf. A069202.
Sequence in context: A108918 A118320 A082334 * A175911 A110338 A171018
Adjacent sequences: A151746 A151747 A151748 * A151750 A151751 A151752
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 17 2009
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2009
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