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A276229
a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=0, a(1)=0, a(2)=1.
1
0, 0, 1, -1, -1, 4, -3, -6, 16, -7, -31, 61, -6, -147, 220, 68, -655, 739, 639, -2772, 2233, 3950, -11188, 5521, 20805, -43035, 6946, 99929, -156856, -36056, 449697, -534441, -401009, 1919588, -1652011, -2588174, 7811784, -4287447, -13924295, 30310973
OFFSET
0,6
COMMENTS
Essentially the same as A077978. - Georg Fischer, Oct 02 2018
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
Sequence in context: A328650 A343891 A232328 * A077955 A077978 A192986
KEYWORD
sign,easy
AUTHOR
G. C. Greubel, Aug 24 2016
STATUS
approved