

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
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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(k1) are specified initial terms. Many further examples of such sequences could be added to the OEIS!


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000
A. M. Amleh et al., On Some Difference Equations with Eventually Periodic Solutions, J. Math. Anal. Appl., 223 (1998), 196215.
J. Greene, The Unboundedness of a Family of Difference Equations Over the Integers, Fib. Q., 46/47 (2008/2009), 146152.


MAPLE

A151749 := proc(n) option remember; if n <= 1 then 1+2*n; else prev := procname(n1)+procname(n2) ; 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
Adjacent sequences: A151746 A151747 A151748 * A151750 A151751 A151752


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jun 17 2009


EXTENSIONS

More terms from R. J. Mathar, Jun 18 2009


STATUS

approved



