OFFSET
0,5
COMMENTS
0 = a(n)*(+a(n) +2*a(n+1) +2*a(n+2)) -a(n+3)*(2*a(n+1) -2*a(n+2) +a(n+3)) for all n in Z.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,-2,-1,-1).
FORMULA
G.f.: (x + x^3) / (1 - x + 2*x^2 + x^3 + x^4). a(3*n) = 0.
G.f.: 1 / (1-x / (1+x / (1-3*x / (1+4*x / (3+1*x / (2-3*x / (1+2*x))))))).
a(n) = (-1)^n * a(-n) = a(n-1) - 2*a(n-2) - a(n-3) - a(n-4) for all n in Z.
EXAMPLE
G.f. = x + x^2 - 3*x^4 - 5*x^5 + 13*x^7 + 21*x^8 - 55*x^10 - 89*x^11 + ...
MATHEMATICA
a[ n_] := Fibonacci[n] (-1)^Quotient[n, 3] Min[Mod[n, 3], 1];
PROG
(PARI) {a(n) = fibonacci(n) * (-1)^(n\3) * (n%3>0)};
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Mar 02 2019
STATUS
approved