

A264800


NearlyFibonacci 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
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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 nth 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(n1)  a(n2) for n>6.
G.f.: x*(x1)*(x+1)*(x^3+x^2+1) / (x^2+x1).
(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*(x1)*(x+1)*(x^3+x^2+1)/(x^2+x1) + 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



