OFFSET
1,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,0,-1,-1).
FORMULA
a(n) = F(n) - D(n+1), where F is the Fibonacci sequence (A000045) and D is "A double Fibonacci sequence" (A103609).
G.f.: x^3*(1+x-x^2) / ((1-x-x^2)*(1-x^2-x^4)). - Colin Barker, Oct 13 2014
EXAMPLE
a(7)=10 because F(7)=13 and D(8)=3 and a(7)=F(7)-D(8).
MATHEMATICA
LinearRecurrence[{1, 2, -1, 0, -1, -1}, {0, 0, 1, 2, 3, 6}, 40] (* James C. McMahon, Oct 17 2024 *)
PROG
(PARI) concat([0, 0], Vec(-x^3*(x^2-x-1)/((x^2+x-1)*(x^4+x^2-1)) + O(x^100))) \\ Colin Barker, Oct 13 2014
(Magma)
A121364:= func< n | Fibonacci(n) - Fibonacci(Floor((n+1)/2)) >;
[A121364(n): n in [1..70]]; // G. C. Greubel, Oct 23 2024
(SageMath)
def A121364(n): return fibonacci(n) - fibonacci((n+1)//2)
[A121364(n) for n in range(1, 71)] # G. C. Greubel, Oct 23 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Graeme McRae, Jul 23 2006
EXTENSIONS
More terms from Colin Barker, Oct 13 2014
STATUS
approved