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A135530
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a(n)=a(n-1)+2a(n-2)-2a(n-3).
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10
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2, 1, 4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, 262144, 1048576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,2).
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FORMULA
| O.g.f.: -(2+x)/(2*x^2-1). a(n)= 2*a(n-2). a(n) = A077957(n+1)+A077957(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2008
a(n)=2^[(1/2)*n]+(-sqrt(2))^n-(1/4)*sqrt(2)*(-sqrt(2))^n+(1/4)*2^[(1/2)*n]*sqrt(2) - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 06 2008
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MATHEMATICA
| CoefficientList[Series[(-x-2)/(2x^2-1), {x, 0, 40}], x]
Transpose[NestList[{#[[2]], Last[#], Last[#]+2#[[2]]-2First[#]}&, {2, 1, 4}, 45]][[1]] (* From Harvey P. Dale, Mar 05 2011 *)
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PROG
| (PARI) a(n)=1<<(1-n%2+n\2) \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| Sequence in context: A117000 A082392 A085086 * A137206 A076736 A182906
Adjacent sequences: A135527 A135528 A135529 * A135531 A135532 A135533
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Feb 20 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2008
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