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A112455
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a(n) = -a(n-2)-a(n-3).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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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FORMULA
| a(n)= - trace({{0, 0, -1}, {1, 0, -1}, {0, 1, 0}})^n - Artur Jasinski (grafix(AT)csl.pl), Jan 10 2007
G.f.: -(3+x^2)/(1+x^2+x^3). a(n) = -3*A077962(n)-A077962(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009]
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MAPLE
| Table[ -Tr[MatrixPower[{{0, 0, -1}, {1, 0, -1}, {0, 1, 0}}, n]], {n, 1, 50}] - Artur Jasinski (grafix(AT)csl.pl), Jan 10 2007
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CROSSREFS
| Cf. A001608, A112458.
Sequence in context: A119493 A032531 A143394 * A001608 A159977 A177461
Adjacent sequences: A112452 A112453 A112454 * A112456 A112457 A112458
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KEYWORD
| sign
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AUTHOR
| Anthony C Robin (anthony_robin(AT)hotmail.com), Dec 13 2005
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Jan 25 2006
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