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A112455
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a(n) = -a(n-2) - a(n-3).
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4
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-3, 0, 2, 3, -2, -5, -1, 7, 6, -6, -13, 0, 19, 13, -19, -32, 6, 51, 26, -57, -77, 31, 134, 46, -165, -180, 119, 345, 61, -464, -406, 403, 870, 3, -1273, -873, 1270, 2146, -397, -3416, -1749, 3813, 5165, -2064, -8978, -3101, 11042, 12079, -7941
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OFFSET
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0,1
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COMMENTS
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This sequence resembles the Perrin sequence, A001608. Like many such sequences with a(1)=0, any prime p divides a(p). The first pseudoprime (composite n divides a(n)) is 121.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,-1,-1).
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FORMULA
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a(n)= - trace({{0, 0, -1}, {1, 0, -1}, {0, 1, 0}})^n. - Artur Jasinski, Jan 10 2007
From R. J. Mathar, Oct 24 2009: (Start)
G.f.: -(3+x^2)/(1+x^2+x^3).
a(n) = -3*A077962(n) - A077962(n-2). (End)
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MATHEMATICA
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Table[ -Tr[MatrixPower[{{0, 0, -1}, {1, 0, -1}, {0, 1, 0}}, n]], {n, 1, 60}] (* Artur Jasinski, Jan 10 2007 *)
LinearRecurrence[{0, -1, -1}, {-3, 0, 2}, 60] (* G. C. Greubel, May 19 2019 *)
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PROG
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(PARI) Vec(-(3+x^2)/(1+x^2+x^3)+O(x^60)) \\ Charles R Greathouse IV, May 15 2013
(MAGMA) I:=[-3, 0, 2]; [n le 3 select I[n] else -Self(n-2) -Self(n-3): n in [1..60]]; // G. C. Greubel, May 19 2019
(Sage) (-(3+x^2)/(1+x^2+x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, May 19 2019
(GAP) a:=[-3, 0, 2];; for n in [4..60] do a[n]:=-a[n-2]-a[n-3]; od; a; # G. C. Greubel, May 19 2019
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CROSSREFS
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Cf. A001608, A112458.
Sequence in context: A301430 A328311 A143394 * A001608 A159977 A245251
Adjacent sequences: A112452 A112453 A112454 * A112456 A112457 A112458
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KEYWORD
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sign,easy
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AUTHOR
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Anthony C Robin, Dec 13 2005
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EXTENSIONS
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Edited by Don Reble, Jan 25 2006
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STATUS
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approved
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