A303427 Interleaved Lucas and Fibonacci numbers.

2, 0, 1, 1, 3, 1, 4, 2, 7, 3, 11, 5, 18, 8, 29, 13, 47, 21, 76, 34, 123, 55, 199, 89, 322, 144, 521, 233, 843, 377, 1364, 610, 2207, 987, 3571, 1597, 5778, 2584, 9349, 4181, 15127, 6765, 24476, 10946, 39603, 17711, 64079, 28657, 103682, 46368, 167761

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

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

G.f.: -(x+1)*(x^2-2*x+2)/(x^4+x^2-1). - Alois P. Heinz, Apr 23 2018

Example

a(8) = Lucas(4) = 7;
a(9) = Fibonacci(4) = 3.

Maple

a:= n-> (<<0|1>, <1|1>>^iquo(n, 2, 'r'). <<2*(1-r), 1>>)[1, 1]:
seq(a(n), n=0..60);  # Alois P. Heinz, Apr 23 2018

Mathematica

LinearRecurrence[{0, 1, 0, 1}, {2, 0, 1, 1}, 60] (* Vincenzo Librandi, Apr 25 2018 *)
With[{nn=30}, Riffle[LucasL[Range[0, nn]], Fibonacci[Range[0, nn]]]] (* Harvey P. Dale, Feb 25 2021 *)

Prog

(MATLAB)
F = zeros(1, N);
L = ones(1, N);
F(2) = 1;
L(1) = 2
for  n = 3:N
    F(n) = F(n-1) + F(n-2);
    L(n) = L(n-1) + L(n-2);
end
A = F;
B = L;
C=[B; A];
C=C(:)';
C
(Magma) [IsEven(n) select Lucas(n div 2) else Fibonacci((n-1) div 2): n in [0..70]]; // Vincenzo Librandi, Apr 25 2018
(PARI) a(n) = if(n%2, fibonacci(n\2), fibonacci(n/2-1)+fibonacci(n/2+1)); \\ Altug Alkan, Apr 25 2018

Crossrefs

Cf. A000045, A000032, A302126.

Sequence in context: A288002 A140129 A029347 * A176076 A058725 A068446

Adjacent sequences: A303424 A303425 A303426 * A303428 A303429 A303430

Keyword

nonn,easy

Author

Craig P. White, Apr 23 2018

Status

approved