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A094014
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Expansion of (1-2*x)/(1-8*x^2).
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6
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1, -2, 8, -16, 64, -128, 512, -1024, 4096, -8192, 32768, -65536, 262144, -524288, 2097152, -4194304, 16777216, -33554432, 134217728, -268435456, 1073741824, -2147483648, 8589934592, -17179869184, 68719476736, -137438953472
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OFFSET
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0,2
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COMMENTS
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Second inverse binomial transform of A094013. Third inverse binomial transform of A000129(2n-1).
The unsigned sequence has g.f. (1+2*x)/(1-8*x^2) and abs(a(n)) = 2^(3*n/2)*(1/2 + sqrt(2)/4 + (1/2 - sqrt(2)/4)*(-1)^n).
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LINKS
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FORMULA
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a(n) = (2*sqrt(2))^n*(1/2 - sqrt(2)/4) + (-2*sqrt(2))^n*(1/2 + sqrt(2)/4).
E.g.f.: cosh(2*sqrt(2)*x) - (1/sqrt(2))*sinh(2*sqrt(2)*x). - G. C. Greubel, Dec 04 2021
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MATHEMATICA
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LinearRecurrence[{0, 8}, {1, -2}, 40] (* G. C. Greubel, Dec 04 2021 *)
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PROG
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(Magma) [n le 2 select (-2)^(n-1) else 8*Self(n-2): n in [1..41]]; // G. C. Greubel, Dec 04 2021
(Sage) [(-2)^n*2^(n//2) for n in (0..40)] # G. C. Greubel, Dec 04 2021
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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