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A123335
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a(0)=1, a(1)=-1, a(n)=-2*a(n-1)+a(n-2)for n>1 .
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-2,1)
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| 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}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
a(n) = A077985(n)+A077985(n-1). - R. J. Mathar, Mar 28 2011
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MATHEMATICA
| LinearRecurrence[{-2, 1}, {1, -1}, 40] (* From Harvey P. Dale, Nov 03 2011 *)
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CROSSREFS
| Sequence in context: A089737 A001333 A078057 * A089742 A187258 A131721
Adjacent sequences: A123332 A123333 A123334 * A123336 A123337 A123338
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KEYWORD
| easy,sign
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 27 2007
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EXTENSIONS
| Corrected by N. J. A. Sloane (njas(AT)research.att.com), Oct 05 2008
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