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

Author

Clark Kimberling, May 10 2016

Keywords

• nonn
• easy

Comments

Every term is a Fibonacci number (A000045).

Examples

			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,...).
		

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).

Crossrefs

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

Programs

Mathematica

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

PARI

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

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