OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
FORMULA
a(n) = 3*a(n-2) - a(n-4) for n>3. G.f.: -x*(x-2) / ((x^2-x-1)*(x^2+x-1)). [Colin Barker, Feb 02 2013]
From Vladimir Reshetnikov, Sep 24 2016: (Start)
a(n) = Sum_{k=1..n} (-1)^(k+1) * Fibonacci(k) * Lucas(n-k).
MATHEMATICA
Differences[Flatten[{Last[#], First[#]}&/@Partition[Fibonacci[ Range[ 40]], 2]]] (* or *) LinearRecurrence[{0, 3, 0, -1}, {0, 2, -1, 6}, 40] (* Harvey P. Dale, Sep 16 2013 *)
Table[(LucasL[n] - (-1)^n Fibonacci[n + 3])/2, {n, 0, 40}] (* Vladimir Reshetnikov, Sep 24 2016 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Mar 03 2008
EXTENSIONS
More terms from Colin Barker, Feb 02 2013
STATUS
approved