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A276228
a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=3, a(1)=-1, a(2)=-3.
2
3, -1, -3, 8, -3, -16, 30, -1, -75, 107, 42, -331, 354, 350, -1389, 1043, 2085, -5560, 2433, 10772, -21198, 2087, 51081, -76453, -23622, 227609, -256818, -222022, 963267, -776041, -1372515, 3887864, -1918875, -7229368, 14954982, -2415121, -34724211, 54509435, 12523866
OFFSET
0,1
LINKS
FORMULA
G.f.: (3 + 2*x + 2*x^2)/(1 + x + 2*x^2 - x^3).
Let (b, c, d) be the three roots of x^3 = 2*x^2 + x + 1, then a(n) = b^(-n) + c^(-n) + d^(-n) = A276225(-n).
a(2*n) = -3*a(2*n-2) - 6*a(2*n-4) + a(2*n-6).
a(n) = 2*A276229(n) + 2*A276229(n+1) + 3*A276229(n+2).
MATHEMATICA
LinearRecurrence[{-1, -2, 1}, {3, -1, -3}, 50]
CoefficientList[Series[(3 + 2 x + 2 x^2)/(1 + x + 2 x^2 - x^3), {x, 0, 38}], x] (* Michael De Vlieger, Aug 25 2016 *)
nxt[{a_, b_, c_}]:={b, c, a-2b-c}; NestList[nxt, {3, -1, -3}, 40][[All, 1]] (* Harvey P. Dale, Dec 19 2022 *)
PROG
(Magma) I:=[3, -1, -3]; [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) Vec((3+2*x+2*x^2)/(1+x+2*x^2-x^3) + O(x^99)) \\ Altug Alkan, Aug 25 2016
CROSSREFS
Sequence in context: A046544 A011088 A352794 * A188938 A156368 A240665
KEYWORD
sign,easy
AUTHOR
G. C. Greubel, Aug 24 2016
EXTENSIONS
Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021
STATUS
approved