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A151749
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.
2
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
OFFSET
0,2
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!
LINKS
A. M. Amleh et al., On Some Difference Equations with Eventually Periodic Solutions, J. Math. Anal. Appl., 223 (1998), 196-215.
J. Greene, The Unboundedness of a Family of Difference Equations Over the Integers, Fib. Q., 46/47 (2008/2009), 146-152.
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) ; # R. J. Mathar, Jun 18 2009
MATHEMATICA
f[{a_, b_}]:=Module[{c=a+b}, If[EvenQ[c], c/2, c]]; Transpose[NestList[ {Last[#], f[#]}&, {1, 3}, 50]][[1]] (* Harvey P. Dale, Oct 12 2011 *)
CROSSREFS
Cf. A069202.
Sequence in context: A082334 A294371 A325985 * A175911 A337405 A304881
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 17 2009
EXTENSIONS
More terms from R. J. Mathar, Jun 18 2009
STATUS
approved