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
KEYWORD
nonn,easy
AUTHOR
Craig P. White, Apr 23 2018
STATUS
approved