A272912 Difference sequence of the sequence A116470 of all distinct Fibonacci numbers and Lucas numbers (A000032).

1, 1, 1, 1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025

Offset

1,5

Comments

Every term is a Fibonacci number (A000045).

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

Formula

From Colin Barker, May 10 2016: (Start)

a(n) = a(n-2)+a(n-4) for n>4.

G.f.: x*(1+x-x^5) / (1-x^2-x^4).

(End)

a(n) = A053602(n-2), n>2. - R. J. Mathar, May 20 2016

a(n) = A123231(n-3), n>3. - Georg Fischer, Oct 23 2018

Example

A116470 = (1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, 76,...), so that (a(n)) = (1,1,1,1,2,1,3,2,5,3,8,5,13,8,12,...).

Mathematica

u = Table[Fibonacci[n], {n, 1, 200}]; v = Table[LucasL[n], {n, 1, 200}];
Take[Differences[Union[u, v]], 100]

Prog

(PARI) Vec(x*(1+x-x^5)/(1-x^2-x^4) + O(x^50)) \\ Colin Barker, May 10 2016

Crossrefs

Cf. A000045, A000032, A116470, A053602, A123231.

Sequence in context: A239881 A051792 A053602 * A123231 A246995 A238782

Adjacent sequences: A272909 A272910 A272911 * A272913 A272914 A272915

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2016

Status

approved