OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,-4,0,0,1).
FORMULA
G.f.: (x + x^2 + 2*x^3 + x^4 - x^5) / (1 + 4*x^3 - x^6).
a(n) = -4 * a(n-3) + a(n-6). a(-n) = (-1)^floor( (n-2) / 3) * a(n) for all n in Z.
a(n) * a(n+3) = a(n+1)^2 - a(n+2)^2 for all n in Z.
EXAMPLE
G.f. = x + x^2 + 2*x^3 - 3*x^4 - 5*x^5 - 8*x^6 + 13*x^7 + 21*x^8 + ...
MATHEMATICA
a[ n_] := (-1)^Quotient[n-1, 3] Fibonacci[n];
CoefficientList[Series[(x + x^2 + 2 x^3 + x^4 - x^5)/(1 + 4 x^3 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 20 2014 *)
PROG
(PARI) {a(n) = (-1)^( (n-1) \ 3) * fibonacci( n)};
(Magma) I:=[0, 1, 1, 2, -3, -5]; [n le 6 select I[n] else -4*Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Jan 20 2014
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Jan 19 2014
STATUS
approved