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A135530
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a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3), with a(0)=2, a(1)=1.
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12
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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
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OFFSET
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0,1
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LINKS
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FORMULA
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O.g.f.: -(2+x)/(2*x^2-1).
a(n) = 2*a(n-2).
E.g.f.: (1/sqrt(2))*( 2*sqrt(2)*cosh(sqrt(2)*x) + sinh(sqrt(2)*x) ). - G. C. Greubel, Oct 17 2016
Sum_{n>=0} 1/a(n) = 3.
Sum_{n>=0} (-1)^(n+1)/a(n) = 1. (End)
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MATHEMATICA
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CoefficientList[Series[(-x-2)/(2x^2-1), {x, 0, 40}], x]
Transpose[NestList[{#[[2]], Last[#], Last[#]+2#[[2]]-2First[#]}&, {2, 1, 4}, 45]][[1]] (* Harvey P. Dale, Mar 05 2011 *)
LinearRecurrence[{0, 2}, {2, 1}, 25] (* G. C. Greubel, Oct 17 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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