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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

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