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A112032
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Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 ...
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8
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4, 1, 8, 2, 16, 4, 32, 8, 64, 16, 128, 32, 256, 64, 512, 128, 1024, 256, 2048, 512, 4096, 1024, 8192, 2048, 16384, 4096, 32768, 8192, 65536, 16384, 131072, 32768, 262144, 65536, 524288, 131072, 1048576, 262144, 2097152, 524288, 4194304, 1048576
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OFFSET
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0,1
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COMMENTS
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lim_{n->infinity} A112031(n)/a(n) = 2/3.
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REFERENCES
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G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148.
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LINKS
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FORMULA
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a(n) = 2^(floor(n/2) + 1 + (-1)^n) = 2^A084964(n).
a(n) = 2*a(n-2).
G.f.: (x+4) / (1-2*x^2). (End)
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MATHEMATICA
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LinearRecurrence[{0, 2}, {4, 1}, 50] (* following conjecture in Formula field above *) (* Harvey P. Dale, Dec 21 2014 *)
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PROG
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(Magma) [2^(Floor(n/2) + 1 + (-1)^n): n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
(PARI) m=50; v=concat([4, 1], vector(m-2)); for(n=3, m, v[n]=2*v[n-2]); v \\ G. C. Greubel, Nov 08 2018
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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