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A029745
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Expansion of (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).
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1
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1, 2, 8, 5, 16, 10, 32, 20, 64, 40, 128, 80, 256, 160, 512, 320, 1024, 640, 2048, 1280, 4096, 2560, 8192, 5120, 16384, 10240, 32768, 20480, 65536, 40960, 131072, 81920, 262144, 163840, 524288, 327680, 1048576, 655360, 2097152, 1310720, 4194304
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OFFSET
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1,2
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COMMENTS
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Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k.
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LINKS
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FORMULA
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G.f.: (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).
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MATHEMATICA
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LinearRecurrence[{0, 2}, {1, 2, 8, 5}, 50] (* or *) With[{nn=20}, Join[{1, 2}, Riffle[ 8*2^Range[0, nn], 5 2^Range[0, nn]]]] (* Harvey P. Dale, Sep 28 2016 *)
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PROG
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(PARI) a(n)=if(n<2, 1+max(-1, n), 2^(n\2)*if(n%2, 5/2, 4))
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CROSSREFS
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Cf. A094958 (numbers of the form 2^k or 5*2^k).
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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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