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.

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

Author

N. J. A. Sloane, Jun 17 2009

Keywords

• nonn
• easy

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

• 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), 196-215.
• J. Greene, The Unboundedness of a Family of Difference Equations Over the Integers, Fib. Q., 46/47 (2008/2009), 146-152.

Crossrefs

Cf. A069202.

Programs

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 *)

Extensions

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