OFFSET
0,6
COMMENTS
Essentially the same as A077978. - Georg Fischer, Oct 02 2018
LINKS
Index entries for linear recurrences with constant coefficients, signature (-1,-2,1).
FORMULA
G.f.: x^2/(1 + x + 2*x^2 - x^3).
Let P = (b-c)*(b-d), Q = (c-b)*(b-d), R = (d-b)*(d-c), (b, c, d) be the three roots of x^3 = 2*x^2 + x + 1, then a(n) = P^(-1)*b^(1-n) + Q^(-1)*c^(1-n) + R^(-1)*d^(1-n).
a(2*n) = -3*a(2*n-2) - 6*a(2*n-4) + a(2*n-6).
MATHEMATICA
LinearRecurrence[{-1, -2, 1}, {0, 0, 1}, 50]
CoefficientList[Series[x^2/(1 + x + 2 x^2 - x^3), {x, 0, 39}], x] (* Michael De Vlieger, Aug 25 2016 *)
PROG
(Magma) I:=[0, 0, 1]; [n le 3 select I[n] else -Self(n-1)- 2*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Aug 25 2016
(PARI) concat([0, 0], Vec(x^2/(1+x+2*x^2-x^3) + O(x^99))) \\ Altug Alkan, Aug 25 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
G. C. Greubel, Aug 24 2016
STATUS
approved