A097594 a(n) = (a(n-1) mod a(n-2)) + a(n-2), a(0) = 3, a(1) = 2.

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, 196418, 121393, 317811, 196418, 514229, 317811, 832040, 514229

Offset: 0

Author

Gerald McGarvey, Aug 29 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

Crossrefs

Cf. A000045, A051792, A053602.

Programs

Magma

[Fibonacci(3 +Floor(n/2) +2*(n mod 2)): n in [0..60]]; // G. C. Greubel, Dec 06 2022

Mathematica

LinearRecurrence[{0,1,0,1}, {2,5,3,8}, 60] (* G. C. Greubel, Dec 06 2022 *)

SageMath

[fibonacci(3 +(n//2) + 2*(n%2)) for n in range(61)] # G. C. Greubel, Dec 06 2022

Formula

a(2n) = Fibonacci(n+4), a(2n+1) = Fibonacci(n+3).

a(n) = A053602(n+6).

a(n) = abs( A051792(n+11) ).

G.f.: (2 + 5*x + x^2 + 3*x^3)/(1 - x^2 - x^4). - G. C. Greubel, Dec 06 2022