OFFSET
0,4
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
FORMULA
G.f.: x*(1+x) / (1-3*x^2+x^4).
a(n) = Fibonacci(n)*(1+(-1)^n)/2 + Fibonacci(n+1)*(1-(-1)^n)/2.
a(n) = (2^(-2-n)*((1-sqrt(5))^n*(-3+sqrt(5)) - (-1-sqrt(5))^n*(-1+sqrt(5)) - (-1+sqrt(5))^n - sqrt(5)*(-1+sqrt(5))^n + 3*(1+sqrt(5))^n + sqrt(5)*(1+sqrt(5))^n))/sqrt(5). - Colin Barker, Mar 28 2016
MATHEMATICA
CoefficientList[Series[x (1 + x)/(1 - 3 x^2 + x^4), {x, 0, 38}], x] (* Michael De Vlieger, Mar 28 2016 *)
PROG
(PARI) concat(0, Vec(x*(1+x)/(1-3*x^2+x^4) + O(x^50))) \\ Colin Barker, Mar 28 2016
(Magma) [Fibonacci(n)*(1+(-1)^n)/2 + Fibonacci(n+1)*(1-(-1)^n)/2: n in [0..40]]; // Vincenzo Librandi, Mar 29 2016
CROSSREFS
KEYWORD
easy,less,nonn
AUTHOR
Paul Barry, May 26 2004
STATUS
approved