This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A264800 Nearly-Fibonacci sequence. 2
 1, 1, 2, 4, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Generate a tree T by these rules: 0 is in T, and if x is in T, then x+1 and -2x are in T, with duplicates deleted as they occur; see A264799. Let g(0) = {0}, g(1) = {1}, g(2) = {-2,2}, g(3) = {-4,-1,3,4}, etc. The number |g(n)| of numbers in the n-th generation of T is a Fibonacci number except for g(3). LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA a(n) = F(n) for 1 <= n <= 3 and n >= 5, and a(4) = 4; where F = A000045, the Fibonacci numbers. From Colin Barker, Nov 25 2015: (Start) a(n) = a(n-1) - a(n-2) for n>6. G.f.: x*(x-1)*(x+1)*(x^3+x^2+1) / (x^2+x-1). (End) MATHEMATICA z = 10; t = Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, -2*#} &, #], 1]] &, {0}, z]]; s[0] = t[[1]]; s[n_] := s[n] = Union[t[[n]], s[n - 1]]; g[n_] := Complement[s[n], s[n - 1]]; g[1] = {0}; Table[Length[g[k]], {k, 1, z}]  (* A264800 *) u = Table[g[k], {k, 1, z}] Flatten[u] (* A264799 *) PROG (PARI) Vec(x*(x-1)*(x+1)*(x^3+x^2+1)/(x^2+x-1) + O(x^100)) \\ Colin Barker, Nov 25 2015 CROSSREFS Cf. A264799, A000045. Sequence in context: A164571 A238589 A288668 * A293189 A278695 A105134 Adjacent sequences:  A264797 A264798 A264799 * A264801 A264802 A264803 KEYWORD nonn,easy AUTHOR Clark Kimberling, Nov 25 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)