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A123335
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a(n) = -2*a(n-1)+a(n-2) for n>1, a(0)=1, a(1)=-1.
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4
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1, -1, 3, -7, 17, -41, 99, -239, 577, -1393, 3363, -8119, 19601, -47321, 114243, -275807, 665857, -1607521, 3880899, -9369319, 22619537, -54608393, 131836323, -318281039, 768398401, -1855077841, 4478554083, -10812186007, 26102926097, -63018038201, 152139002499
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OFFSET
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0,3
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COMMENTS
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Inverse binomial transform of A077957 .
The inverse of the g.f. is 3-x-2/(1+x) which generates 1, 1, -2, +2, -2, +2,... (-2, +2 periodically continued). - Gary W. Adamson, Jan 10 2011
Pisano period lengths: 1, 1, 8, 4, 12, 8, 6, 4, 24, 12, 24, 8, 28, 6, 24, 8, 16, 24, 40, 12,... - R. J. Mathar, Aug 10 2012
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (-2,1).
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FORMULA
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a(n) = (-1)^n*A001333(n).
G.f.: (1+x)/(1+2*x-x^2).
a(n) = 1/2*((-1-sqrt(2))^n+(-1+sqrt(2))^n). [Paolo P. Lava, Nov 19 2008]
a(n) = A077985(n)+A077985(n-1). - R. J. Mathar, Mar 28 2011
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MATHEMATICA
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LinearRecurrence[{-2, 1}, {1, -1}, 40] (* From Harvey P. Dale, Nov 03 2011 *)
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CROSSREFS
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Sequence in context: A077851 A089737 A001333 * A078057 A089742 A187258
Adjacent sequences: A123332 A123333 A123334 * A123336 A123337 A123338
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KEYWORD
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sign,easy
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AUTHOR
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Philippe DELEHAM, Jun 27 2007
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EXTENSIONS
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Corrected by N. J. A. Sloane, Oct 05 2008
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STATUS
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approved
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